IPhT Institut de Physique Théorique de Saclay Rapport d'activité juin

IPhT

Institut de Physique Théorique

de Saclay

Rapport d'activité

juin 2007 mai 2011

Commissariat à l'énergie atomiqueet aux énergies alternatives

Direction des sciences de la matièreCEA / DSM / IPhT

Centre national de la recherche scientiqueInstitut de physique

CNRS / INP / URA 2306

CEA Saclay, 91191 Gif-sur-Yvette, Francehttp://ipht.cea.fr/ - Tel: +33 (0)1 69 08 73 85

2 Rapport d'activité CEA/DSM/IPhT 2007 2011

Contents

Foreword 5

A Mathematical physics 13

B Cosmology and particle physics 73

C Statistical physics and condensed matter 131

D Appendices 185

3


Foreword

This report presents an overview of the activities of the Institut de Physique Théo-rique (IPhT) from June 2007 to May 2011.

Over this four years period, more than 700 papers have been published by IPhTmembers (permanent researchers, PhDs and PostDocs, long term visitors). All theseworks are surveyed in the three scientic parts of the report : Models and Structures: Mathematical Physics Cosmology and Particle Physics Statistical Physics, Condensed Matter and BiophysicsEach part starts with an overview that should help the interested reader to nd itsway to the more technical details. The separation in three main themes is partlyarticial, and the same people often contribute to several chapters.

The writing of the scientic part involved all the permanents members of the lab.These individual contributions were collected by a team of volunteers and thenpassed to the three editors who also had the charge to write the overviews. Eachlevel involved a good amount of polishing, and I thank all the participants for theirworks. The three editors, Didina Serban, Stéphane Lavignac and Olivier Parcolletdeserve a special mention.

The last part describes others facets of the IPhT: awards, teaching, externalfundings, scientic editing, research administration, organization... My deputies,Anne Capdepon and Olivier Golinelli, dedicated a lot of time to it.

Many things have happened in France and in the world during the last four years,several of them being quite dramatic. Though what happened at IPhT is doomed tobe anecdotal in this perspective, the Institute changed at an accelerated pace, andthe impact of some of the world scale events can be seen clearly on French researchand in particular at IPhT. The following remarks are an attempt to describe and(hopefully) understand the situation of the IPhT today and the stakes for tomorrow.

Expansion

One important trend is expansion. Over the period under review, a single CEAphysicist retired, two juniors where hired and one senior moved to IPhT. On theCNRS side, three physicists have retired and one has left academic research, mean-while four junior physicists were hired, and one senior moved to IPhT. Though thenumber of permanent members has raised only marginally, the number of studentsand PostDocs is still progressing very fast. It has increased by a factor of 4 or 5over the last ten years, and now represents about half of the crew. Moreover, thenumber of visitors (from one day visitors to sabbaticals, from trainees to permanentsin neighboring institutions spending part of their time at IPhT,...) is also expanding

5


rapidly: having 120 people around is now a common situation.

Concerning the evolution for the next ten years, another important fact willsuperpose to this expansion. In 2010, new rules for retirements have been adoptedby the French chambers. Up to 2009, special agreements forced CEA employeesto retire at the age of 60. Most physicists of this age argue with reason that theyare still able to produce high quality research, and IPhT has always found meansto allow them to pursue their work in good material conditions. The new horizonis now the age of 70. Budget forecasts indicate that the number of permanents atIPhT will not increase (an euphemism). A mechanical consequence is a period ofabout ten years with very few hirings on the CEA side. This is unavoidable, butdestabilizes noticeably the age pyramid of the Institute. Arguably, this is partlycompensated by fresh blood coming from students, PostDocs and possibly hiringsat CNRS.

External fundings

Another trend is the increasing importance of external fundings. Ten years ago,external fundings where totally marginal. In 2011, more than 75% of our PostDocsare paid on external fundings, this is also the situation for invitations and travels.External fundings have become vital for the Institute. They come from a number ofsources. Europe is by far our main provider, via Marie Curie programs and EuropeanResearch Council (ERC) grants. Then comes the French Agence Nationale de laRecherche (ANR). Several more targeted sources (fundings for scientic exchangeswith specic countries,...) come as complements.

But other sources of funding should take an important role in the near future,via large structures that have come to life in France recently. One of their goals is tomake French main research areas more visible from the outside world. They regrouphundreds to thousands of researchers on specic themes. This started a few yearsago with the so-called Réseaux Thématiques de Recherche Avancée. But the majorstep was the launch in 2010 of the Grand emprunt de la France : Investissementd'avenir (a reaction to the nancial crisis since 2008) which is deeply reshapingthe landscape of French research. Under the ag of excellence, new structurescalled Idex, Equipex, Labex (the generic name *ex is used in the sequel) are inthe process of labeling.

A short aside is in order. It is hard to (over)estimate the impact that these newstructures have had or will have on the more traditional entities devoted to sciencein France, CNRS and CEA to quote only the ones most relevant for the IPhT. Infact the name external funding is by opposition to means coming from CEA orCNRS. These two organisms still cover the salaries of permanents of the IPhT. Theyalso provide access to reviews. CEA provides the buildings and working environ-nement. Some predict that in the short or middle term these will be their sole roles.CEA (mainly) and CNRS still contribute signicantly to direct scientic activities(invitations, missions, conferences) but this is steadily decreasing. Obviously, thenew structures will sooner or later have a dominant position to orient the scienticpolicy of the French research. This situation is a source of worry for both CEAemployees (36 physicists and 8 persons in the support group) and CNRS members(16 physicists) at IPhT. In the past years, the CNRS has been re-organized severaltimes, possibly to adapt to this new situation. In the same period, the CEA has

Contents 7

not experienced such jolts, but its implication in the new structures is a clear signthat important changes are on their way. There will also be consequences on the re-lations between the IPhT and the University, though it is too early to know exactlywhich ones. There is denitely room for improvements. Let me just note that IPhTharbors already a few professors (or assistant professors) for part of their research,that several IPhT members have a notable investment in teaching, but that manymore would like to teach and lack opportunities.

IPhT is directly involved in two successful Labex. P2IO, Physique des deuxinnis et des origines covers our activities in particle physics and astrophysics.PALM, Physique : Atomes, Lumière, Matière covers our activities in statisticalmechanics, condensed matter physics and biophysics. Our activities in mathematicalphysics participate to the Fondation mathématique Jacques Hadamard which wasnot selected as a Labex in the rst round, but which had already received a thoroughgovernmental funding.

The members and/or teams at IPhT have in fact been remarkably successfulin garnering all kind of fundings. The most spectacular record is for the highlycompetitive ERC grants. Four of them began during the period under review,and four more will begin soon, leading to a total of six starting grants and twoadvanced grants at IPhT. A ninth ERC laureate spends part of her time at IPhT onan excellentia University/CEA chair. The successes at ANR are also very noticeable.Let us just quote, among the almost twenty ANR contracts at the institute, thethree ANR excellentia chairs attributed to three recently recruited members. Thesesuccesses are obviously the main reason for the important expansion of the Institute,which should go on for another four or ve years at least, and more generally for itsvisibility and attractiveness.

Closer to experiment

A third important trend is to get closer to experiments. This is particularlystriking in Cosmology and Particle Physics. The role of the LHC is of course im-portant, but many other present or future instruments (RHIC, Planck, Lisa,...) mo-bilize IPhT teams. The tendency is also visible in Statistical Mechanics (structuralglasses, granular materials,...), Condensed Matter (new materials, heavy fermions,graphene,...) and Biophysics (motors, structure prediction, sequence alignment,...).It is clear enough from this short description that the situation is hardly compara-ble because experiments in high energy physics and condensed matter have totallydierent scales (time, cost,...).To get closer to experiments, the birth of the *ex structures could have a signicantfavorable incidence in the future, because they incorporate theoretical physicists instructures involving a fair majority of instrumentalists and because one of their goalsis to allow transverse research.

Coding

Finally, the importance of computer science related activities has raised signif-icantly since the previous report. This goes from web-servers for biophysics tosoftware for condensed matter physics, precision gauge theory computations or cos-mology and astroparticles. There is of course a long history of numerical compu-tation and simulation in Physics, but there is a clear shift in the approach. The


aim is not simply to have a running code for an individual, a team or a communityanymore, but to produce/furnish a real software compliant with software standards.Portability and durability imply a need for clarity, simplicity, readability, generalityand modularity of the code. This is getting more and more important in physics,and is probably going to lead to some new specializations in a near future. There isstill plenty of room for good physicists inventing good algorithms, because historyshows that progress in computing hard problems often (if not always) comes froma better understanding of the physics. But these new creative algorithms have tobe implemented respecting professional coding standards and without wasting timein reinventing the standard algorithms. This requires close contacts between physi-cists and computer scientists. A short term tendency seems to rely for this parton students or PostDocs coming from computer science but with a background inphysics.

Excellentia

As the reader will surely have noticed, excellence is the buzzword these days,and it is meant to become a label, hence possibly also a Grail, at all scales fromindividuals to vast geographic areas. It is timely to try to explain the position andsituation of the IPhT.

I surely do hope that the review of the external committee will conclude that,averaged over the Institute, the result is indeed excellent. What I know for sureis that people at IPhT (and elsewhere in the other scientic institutions for thatmatters) do their very best to produce excellent research. The question is more onhow much energy we should put in to get excellentia labels. In the near future theselabels will clearly bring more money, but will also imply changes in our workinghabits. So the position of the IPhT, which can clearly not be represented by theposition of its director alone, is contrasted. Some of us feel that we have no choicebut to enter basically every competition, while some other would accept some cuts(in money, invitations, travels) to preserve the tranquility and comfort they need towork best. There is a spectrum of intermediate positions.

One can interpret some of the changes at the IPhT (and possibly more generally inFrench research) over the last decade or so, as a metaphor of economic globalization.Some people argue that this passage was totally unavoidable. As the history of realeconomy shows, even if this is true in average, it does not mean that all otherstrategies were doomed to failure: in some places original niche strategies have been(even more) successful. In fact, the IPhT had a number of specicities (some wouldsay eccentricities) that made it world famous and could have made it a successfulcandidate for alternative development models. One could even argue that some ofthe evolutions developed at the cost of part of our originality. It is nevertheless afact that in the nineties, the IPhT engaged rmly in a series of important changes,starting with the implementation of a regular review by an international scienticcommittee and (soon after) of a new, open, hiring procedure. The situation todayis clearly very inuenced by this move, for obvious reasons. Most of the members ofthe international scientic committees and of the people hired since 1995 had beenexposed early to the American (or close to American) research systems. They ndit natural to apply for grants and to build a group of students and PostDocs aroundthem. But the older IPhT philosophy, often based on close collaborations amongpermanents, is still vivid.

Contents 9

Highlights

Compared to other entities devoted to theoretical physics worldwide, the IPhT isamongst the giants, with more than 50 permanent researchers (36 are CEA employ-ees and 16 are CNRS members). Its basic aim is contribute to a better understandingof the laws of nature, from the largest scales to the smallest ones. This goal cantake a variety of incarnations, depending on the eld of research and the personalityof the researcher. But the IPhT can claim to harbor at least one respected special-ist in most of the important physics themes of current interest. This is one of it'snotable specicities, maybe one that could be preserved despite the many changesand uncertainties of the future. Among the obvious benets is the possibility, andeven incentive, of cross fertilization among dierent elds.

The Institute disposes of several task forces of leading experts.

One example is the eld of precision perturbative quantum gauge eld theorycomputations. This eld is living a revolution that started about a decade ago andstill goes on. The LHC makes this activity particularly timely because high precisionbackground subtraction is needed to get at the new physics expected there. Theactivity at IPhT goes from abstract (but deep) results relating gauge theory andgravity amplitudes to more concrete (but highly tricky) computations of standardmodel cross sections. The intermediates are numerous, there is impressive math-ematics in each, and the ow of ideas if by no means one-way. The output is amixture of standard publications and practical software. These activities also haveclose connections with integrable systems a tradition at IPhT - used to computethe spectrum of supersymmetric gauge theory, and of course with string theory.

String theory is a rather recent direction taken by the IPhT. After several failuresto attract seniors, the policy to build a junior group is by now a real success. Thegroup cannot cover all aspects of the subject, but its members have made funda-mental contributions to black holes, ux compactications, ADS/CFT and manymore.

Another example of a considerable task force at IPhT is the group studying non-perturbative aspects of QCD, extremely competitive in all aspects of this domain,with the notable exception of lattice computations.

A large human quota is also devoted to physics beyond the standard model,astroparticles and cosmology. At IPhT perhaps more than elsewhere these subjectsare close cousins because of the number of cross-collaborations. This activity hasbeneted from a number of recruitments in the recent past, and its dynamics is anevidence.

Condensed matter physics is also a huge theme that the IPhT integrated to itsscientic policy only recently. This resulted in the recruitment of three physicists, alljunior at that time. This small group was able to provide a technology watch andin particular interact strongly with the other rather large condensed matter physicsgroups nearby and with other members of the IPhT. This has led to a number ofnotable contributions. The recent emergence of AdS/CFT methods in condensedmatter was a good opportunity to create new contacts within the Institute.

A number of IPhT members also devote a lot of attention to another very im-portant recent subject, out of equilibrium statistical physics, either via works onparadigmatic models, or via general exact out-of equilibrium relations, or nallyvia concrete applications for instance to biology. This activity is also close to com-


plex systems in general, disordered systems and spin glasses. The attention is nowfocusing on granular materials and structural glasses.

Among the obvious absences of the IPhT, the Institute cannot claim to have agroup working on biophysics. However, a number of physicists have a deep interestin biology (and this is a tradition in fact) resulting in a number of important contri-butions, ranging from biology-inspired theoretical physics to theoretical physicsapplied to biology and used by biologists.

Other activities can progress signicantly by the eorts of a few.Mathematical physics has seen some of its representatives get closer to pure math-

ematics, with great success. One can note the works on dynamical systems and quan-tum chaos but visible contributions to important combinatorial, probabilistic andalgebraic geometry problems also come to mind: planar maps, Razumov-Stroganovtype conjectures, cluster algebras, Eynard-Orantin equations coming from randommatrix theory, quantum gravity.

As shown by work done at the Institute, random geometry can also be a fruitfulpath to a better understanding of non-unitary quantum eld theories, conformalor massive, via logarithmic conformal eld theories and super sigma models, withconcrete applications in condensed matter.

A fair proportion of the IPhT production made its way in the top 10% or top1% most cited in Physics over the period 2007-2011. Some papers have had thehonor of the front-cover of good journals or have been awarded prizes. This is ofcourse a valuable way of counting merits, but there are others that require moreunderstanding and long term view. Clearly I'm far from having these two qualitieson the full spectrum of the activities at IPhT. Needless to say, reading the report gaveme the feeling that many remarkable works have been going on in the Institute. ButI nd it impossible to propose a fair list of highlights for the scientic achievementsat IPhT during the last four years. This is probably best left to the judgment ofthe visiting committee.

Challenges for the future

The rst and clearest challenge for the future is the quality and originality ofresearch, either measured by the excellentia or by other traits. Though only thefuture can tell, the reading of this report gives me strong reasons to be condent. Ihope other readers will share this view.

Though we are used to attribute human traits to abstract entities, it is excessive toview the good work done at IPhT as a scientic success of the IPhT. My predecessors,with the help of internal and external scientic committees, deserve credit to havehired and brought together good people, creating a general environment propitiousto good science. But from then on, whatever is done is done by individuals, or verysmall groups. So the main challenge is for individuals.

To make good research, one of the important tools today is funding. Again, thereare good reasons to be condent, and again, this important challenge is mainly forindividuals because this is how funding (especially in theoretical physics) is oftentargeted.

Research is partly a lonesome activity, and this reinforces the human tendencyto attribute our successes to ourselves, and our failures to external circumstances.For this reason and for many others, it is not surprising that the two individual

Contents 11

challenges lead to a cascade of challenges for the administration of the IPhT (moreglobally, of the Direction des Sciences de la Matière, of the CEA,...). Here is anon-exhaustive list.

The main managing tool for a scientic policy is recruitment, either permanentpositions or long-term visitors. On this front, the situation is alarming. As alreadymentioned, the question of permanent positions is relegated to the middle or eventhe long term. This should incite us to be even more careful in the choice of PostDocsand long term visitors. But by now the money to pay these visitors comes mostlyfrom targeted individual grants. If the needs t with a grant goals, I'm condentthat the grant holder will make clever choices. But a view at the level of the Instituteis crucial as well. For instance, what was done about a decade ago for string theoryand condensed matter, namely the creation ex nihilo of a group, would be totallyimpossible today. The possibility of creating a biophysics group is an example of animportant issue that has to be postponed.

The diversication of nancial resources over the last years has mechanically ledto an explosion of administrative tasks. The recent hardenings of the implementationof the French employment law have amplied this tendency. The number of thingsto do, but also their complexity, are at least an order of magnitude higher thanit was ten years ago. The situation is critical. The dedication and skill of ouradministrative group, plus the aectation of more and more time and energy of thedeputy directors of the IPhT to these tasks (at the cost of neglecting other importantissues) are reaching their limits. The same observations apply probably at higherlevels in the CEA.

As already mentioned, the number of people present daily at IPhT well exceeds100, and we are in an urgent need for a macroscopic raise of the number of oces. Itis to be noted that, in the meantime, people not interested in getting funding sharethe inconveniences with people having funding for a number of visitors. The qualityof life, at least if measured by the area per physicist, is deteriorating rapidly. Butspatial extension comes with another challenge: the population of the IPhT is notonly larger, but also more and more heterogeneous, with people coming from diversehorizons and expecting to spend a limited period in the Institute. A risk of phaseseparation is emerging, people with the same interests demanding to occupy neigh-boring oces. At the same time, the new *ex structures will sooner or later createan incentive for both permanent and non-permanent people to be more delocalized.Good or bad, these tendencies are new at IPhT and requires some thinking.

There is a slow shift from the old situation, when the IPhT was overwhelminglypopulated by permanent researchers, to a situation closer to what is considered asnormal abroad, when the IPhT will harvest a much smaller number of permanentswith an army of non-permanents (PhD students, PostDocs, ...). This process willtake a long time, and is beyond my horizon, but I would like to make two remarks.While obviously many places over the world manage to do top quality research withsuch a structure, the transition for the IPhT will probably be delicate, and relyingplainly on retirements to decide of the future population of permanents is clearly notthe right thing to do. Precarity is also an issue, and even if this is naive, I do hopethat the non-permanents that will give their best young years to the Institute willdo it in a situation, in France and in the world, when this experience will increasesignicantly their prospects of nding attractive positions, be it in fundamentalresearch or elsewhere.


To summarize, the economy of the future at IPhT will require delicate balances:get fundings for projects but avoid to see our research targeted by fashion; preservecreative thinking without losing sight of stategic management; leave a lot of roomfor individual initiative, but keep a strong feeling for collective interests; oer to allthe members of the Institute permanent or not working conditions that allowthem to give their best.

The devotion of physicists for physics (at IPhT and elsewhere) is the best guar-antee that we shall be able to win the challenges of the future, and I'm already eagerto see how the main challenge for our Institute, the one for scientic inventivenessand originality, will be met in the next years.

Michel Bauer

CHAPTERA

Mathematical physics

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

A.1 Flux compactications . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

A.1.1 Generalized geometry and global aspects . . . . . . . . . . . . . . . . . . 21

A.1.2 Instanton eects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

A.2 Heterotic strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

A.3 Black holes in string theory . . . . . . . . . . . . . . . . . . . . . . . . 23

A.3.1 Supersymmetric black hole microstate geometries . . . . . . . . . . . . . 23

A.3.2 Microstates from string theory . . . . . . . . . . . . . . . . . . . . . . . 24

A.3.3 Kerr/CFT correspondence . . . . . . . . . . . . . . . . . . . . . . . . . . 24

A.3.4 Background dependence of supersymmetric spectra . . . . . . . . . . . . 24

A.3.5 Chronology protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

A.3.6 Multicenter non-BPS black holes . . . . . . . . . . . . . . . . . . . . . . 25

A.3.7 Solutions in pure gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

A.4 Structure of gauge theory and string theory amplitudes . . . . . . . 26

A.4.1 Structure of gauge theory amplitudes . . . . . . . . . . . . . . . . . . . 26

A.4.2 Automorphic properties of string theory in various dimensions . . . . . 26

A.4.3 Perturbative string theory in various dimensions . . . . . . . . . . . . . 27

A.4.4 Asymptotically safe quantum gravity . . . . . . . . . . . . . . . . . . . . 27

A.5 Integrability, AdS/CFT correspondence and the exact spectrum ofthe N = 4 SYM theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

A.5.1 The BES equation and the scaling function . . . . . . . . . . . . . . . . 28

A.5.2 Semiclassical limit and the algebraic curve method . . . . . . . . . . . . 29

A.5.3 The AdS4/CFT3 correspondence . . . . . . . . . . . . . . . . . . . . . . 29

A.5.4 Classical integrability of the coset sigma model . . . . . . . . . . . . . . 30

A.6 Holography and gravity duals . . . . . . . . . . . . . . . . . . . . . . . 30

A.6.1 Supersymmetry breaking in AdS/CFT . . . . . . . . . . . . . . . . . . . 30

A.6.2 New solutions dual to supersymmetric four-dimensional theories . . . . 31

A.7 Enlarging the scope of the AdS/CFT correspondence . . . . . . . . 31

A.7.1 Fundamental issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

A.7.2 Stringy corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

A.7.3 New solutions duals to two-dimensional theories . . . . . . . . . . . . . 32

A.7.4 AdS/CFT for condensed matter applications . . . . . . . . . . . . . . . 32

A.8 Topological recursion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

A.8.1 Topological recursion and matrix models . . . . . . . . . . . . . . . . . . 33

A.8.2 CFT approach to matrix models . . . . . . . . . . . . . . . . . . . . . . 33

A.8.3 Quantization of Riemann surfaces . . . . . . . . . . . . . . . . . . . . . 34

13


A.8.4 Topological recursion, algebraic geometry and topological strings . . . . 34

A.9 Random matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

A.9.1 Large random matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

A.9.2 Matrix models and tau functions . . . . . . . . . . . . . . . . . . . . . . 37

A.9.3 Scattering of folded strings in two-dimensional Minkowski space . . . . 38

A.9.4 The Student ensemble of correlation matrices: eigenvalue spectrum andKullback-Leibler entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

A.10 Random geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

A.10.1 Statistical models on random lattices . . . . . . . . . . . . . . . . . . . . 39

A.10.2 Geometrical critical phenomena, matrix models and 2D gravity . . . . . 39

A.10.3 Distance statistics in random maps . . . . . . . . . . . . . . . . . . . . . 40

A.10.4 Random tree growth by vertex splitting . . . . . . . . . . . . . . . . . . 41

A.11 Liouville quantum gravity and KPZ . . . . . . . . . . . . . . . . . . . 42

A.11.1 Rigorous proof of the KPZ relation . . . . . . . . . . . . . . . . . . . . . 43

A.11.2 Derivation of the geometrical KPZ relations . . . . . . . . . . . . . . . . 43

A.11.3 SLE, KPZ and Liouville quantum gravity . . . . . . . . . . . . . . . . . 44

A.12 Geometrical models and applications . . . . . . . . . . . . . . . . . . 44

A.12.1 Interfaces in 2D statistical mechanics . . . . . . . . . . . . . . . . . . . . 45

A.12.2 Multifractal harmonic measure and winding of random 2D interfaces . . 46

A.12.3 Domain walls and interfaces - again . . . . . . . . . . . . . . . . . . . . 47

A.12.4 Boundary loop models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

A.12.5 Valence bonds and entanglement . . . . . . . . . . . . . . . . . . . . . . 48

A.12.6 Interacting anyons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

A.12.7 Random tilings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

A.12.8 Lattice models of biopolymers . . . . . . . . . . . . . . . . . . . . . . . . 49

A.12.9 Colouring and ow problems . . . . . . . . . . . . . . . . . . . . . . . . 49

A.13 Loop models, integrability and combinatorics . . . . . . . . . . . . . 49

A.13.1 Loop gas, combinatorics, and quantum algebra . . . . . . . . . . . . . . 50

A.13.2 Combinatorics of alternating sign matrices and of Gessel's conjecture . . 51

A.13.3 Limit shapes in tiling/dimer systems . . . . . . . . . . . . . . . . . . . . 52

A.13.4 Discrete integrable systems, quantum spin chains and cluster algebras . 52

A.13.5 Labelled positive paths and matchings . . . . . . . . . . . . . . . . . . . 53

A.14 Sigma models on super-manifold targets: structures and applications 54

A.14.1 Conformal sigma models on supergroups: lines of CFT . . . . . . . . . . 54

A.14.2 CPn+m−1|n models at θ = π: strong coupling physics . . . . . . . . . . 55

A.14.3 RG ows in super Gross Neveu models . . . . . . . . . . . . . . . . . . . 55

A.14.4 Sigma models and loop models . . . . . . . . . . . . . . . . . . . . . . . 56

A.14.5 Logarithmic CFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

A.15 Quantum eld theory on curved spaces . . . . . . . . . . . . . . . . . 56

A.15.1 Field quantization in curved space . . . . . . . . . . . . . . . . . . . . . 56

A.15.2 From startriangle integrals on Lobatchevski space to Källen-Lehmannrepresentations of perturbative two-point functions in the de Sitter universe 57

A.16 Generalized interval exchange maps . . . . . . . . . . . . . . . . . . . 57

A.17 Stochastic dynamical systems . . . . . . . . . . . . . . . . . . . . . . . 57

A.17.1 Dynamical systems subject to general noise . . . . . . . . . . . . . . . . 58

A.17.2 Diusion and multiplication in a random medium . . . . . . . . . . . . . 58

A.17.3 Localization in the non-linear Schrödinger equation . . . . . . . . . . . . 58

A.18 (Magneto-)hydrodynamical instabilities . . . . . . . . . . . . . . . . . 58

A.18.1 Energetic stability of cylindrical dynamos . . . . . . . . . . . . . . . . . 59

A.18.2 Helical dynamos driven by stochastic ows . . . . . . . . . . . . . . . . 59

A.18.3 Strato-rotational instability . . . . . . . . . . . . . . . . . . . . . . . . . 59

A.19 Dynamics of quantum decoherence and random matrix models . . . 59

A.20 Quantum formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Mathematical physics 15

A.21 Scattering theory with nonlocal potentials and complex angular mo-mentum theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

A.22 Nonhermitian quantum chaos . . . . . . . . . . . . . . . . . . . . . . . 60

A.22.1 Resonances for chaotic scattering systems . . . . . . . . . . . . . . . . . 61

A.22.2 Damped quantum systems . . . . . . . . . . . . . . . . . . . . . . . . . . 61

A.23 Quantization and resummation methods in quantum mechanics . . 61

A.23.1 Multi-instantons and exact quantization . . . . . . . . . . . . . . . . . . 61

A.23.2 Orderdependent mapping and the spectrum of V (x) = x2 + i√gx3 . . 61

A.24 Zeta functions over zeros of zeta functions . . . . . . . . . . . . . . . 62

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

Introduction

The research in the group of mathematical physics concerns a wide spectrum oftopics, ranging from string theory, quantum gravity, matrix models, combinatorics,statistical models on xed and random geometries, integrability, conformal eldtheory, quantum eld theory in curved spaces, classical and quantum dynamicalsystems (including eects of noise and non-hermiticity), to number theory. Thesesubjects are deeply interconnected, and they are often using a common ensemble oftools, that gives the group its unity. In many cases, the research reported here isalso closely related with the activity of other groups in our Institute.

We start this introduction with topics related to string theory. If one regards theoverall research landscape that falls under this designation, one can see that, afterthe stream of discoveries of the second superstring revolution and of the AdS/CFTcorrespondence, the eld has divided roughly in three distinct subelds, which,although related technically, are guided by three dierent physical aims.

The rst aim is to relate string theory to the real world, trying to obtain bothphenomenologically-interesting systems, or systems realizing ination or de Sittervacua. A major activity of the IPhT group in this direction is the construction ofcompactications on six-dimensional compact manifolds with ux, of heterotic com-pactications, and the understanding of the supersymmetry-breaking mechanismsthat are proposed to give rise to deSitter vacua in string theory. Topological stringscalculate holomorphic quantities in string compactications, and since topologicalstrings can be related to random matrices, the extensive work done in Saclay onelucidating various aspects of topological strings also falls into this category. Adierently-avored work which falls in the same overall aim is the calculation ofstring and supergravity amplitudes at higher loop order, and the eorts to establishwhether N = 8 supergravity is ultraviolet nite.

The second aim, motivated by the fact that string theory is a theory with a re-markable success in describing black holes, is to investigate whether one can solveor deepen our understanding of longstanding problems of quantum gravity. Theseinclude the information paradox, the protection of chronology, the physics of cosmo-logical singularities, or the microscopic origin of the black hole entropy. Our groupuses a variety of research attack angles here, ranging from the Kerr-CFT corre-spondence and 2D quantum gravity, to constructing and analyzing supersymmetricand nonsupersymmetric multicenter solutions, and using them to test the the recentconjecture that black holes are ensembles of horizonless microstate solutions, or to


see how various black hole indices jump across the walls of marginal stability in themoduli space.

The third aim is to use string theory not as much as a theory to explain thereal world, but rather as a mathematical machinery which, via the AdS-CFT corre-spondence, relates strongly-coupled gauge theories to weakly-coupled string theory.Hence, one can try to use AdS-CFT and string theory as a tool to understand theaspects of the strongly coupled theories that appear in various real-world systems,like the strongly coupled quark-gluon plasma, or condensed-matter systems.

One of the major goals in this area is to use AdS-CFT to describe asymptotically-free gauge theories (like QCD) and for this one needs to understand string theoryin AdS when the curvature is larger than the string scale. The only tool for this isintegrability, and our group works on the integrable structures that appear in theduality between N = 4 Super-Yang-Mills and string theory in AdS5 × S5.

Another important issue tackled in our group is the construction of new gauge-gravity solutions. Those include solutions dual to four-dimensional eld theorieswith less supersymmetry, dual to metastable supersymmetry breaking in three andfour dimensions, dual to the deconnement phase transition in three-dimensionaltheories, or dual to nonconformal lower-dimensional theories similar to those thatappear in describing certain condensed-matter systems.

Yet another research direction concerns string corrections to the AdS-CFT corre-spondence, and whether this correspondence can be derived directly by using CFTarguments. Besides the activity in our group, many members of the particle physicsgroup in our Institute work on using AdS-CFT to describe strongly-interactingquark-gluon plasmas; this activity is reported in section B.17 on gauge-gravity du-ality.

Thematically moving away from string theory somewhat, we come to randommatrix theory. This is one of the traditional elds of activity of the IPhT, whosemembers made seminal contributions over the years. Random matrices arise in manyareas of physics, mathematics, biology, economics.

One of the main results of the pioneereing works of Wigner, Dyson and Methahad been the control of the leading order in the 1/N expansion, where N is thematrix size. Concerning the 1/N expansion, the state of the art has been signif-icantly pushed forward at IPhT. The all-order control of various models has beenobtained, including models with one or more Hermitian matrices, super-matrices,the so called β-ensembles, the chain of matrices, and the O(n) matrix model. It wasalso observed that it computes the large size expansion of various crystalmeltingmodels (also called random partitions, or random plane partitions, or random selfavoiding walks). The results on the 1/N expansion of the matrix models are deeplyrelated to problems in enumerative geometry and in string theory, where one is inter-ested in counting Riemann surfaces with given characteristics (handles, boundaries).The method of topological recursion allows to count the surfaces of higher topologyin terms of number of surfaces with lower topology. It was conjectured that theGromov-Witten invariants in algebraic geometry should also obey the same topo-logical recursion. This would be an important fact, since it would allow an explicitcomputation of those invariants.

The matrix models and integrable models allow one to dene in a very natural way


a quantum version of the Riemannian geometry of surfaces, where the Bethe ansatzequations constitute consistency conditions. Similar properties are investigated inthe context of integrability in AdS/CFT. The consequences of the existence of thisquantum geometry are still under exploration by the researchers in our group.

As an application of random matrices to economy, a new ensemble of random ma-trices related to multivariate Student random variables has been introduced, whosedensity of states ts nicely the density of state of empirical correlation matrices ofrealworld nancial data.

Another, related subject of research is the study of random surfaces, i.e. statis-tical models of discrete matter (spins, particles) on uctuating (random) lattices.This problem is attacked from two complementary directions, namely with randommatrix tools, but also with purely combinatorial techniques. Exploiting the progressof the random matrix theory, many new results have been obtained for statisticallattice models, like the Ising model and of the O(n) models on random lattices ofarbitrary topology. The analysis of the large lattice limits gave rise to new relationswith conformal eld theories and Liouville gravity.

Discrete random surfaces correspond to combinatorial structures called maps,which are also the object of an active research at IPhT, running along two maindirections: the algebraic problem of counting maps (enumeration) and the study oftheir geometry, naturally described by the graph distance. Exploiting the bijectionbetween maps and appropriate decorated trees and the underlying integrable struc-ture, a number of results have been proven concerning the properties of geodesics inthe limit of large random maps.

Random trees are met in many elds of sciences, ranging from social sciences tobiology, physics and computer science. In this context a new class of treegrowthmodels by vertex splitting and attachment has been introduced, motivated by itspossible relation with RNA folding.

Still in the framework of Liouville quantum gravity, the famous KnizhnikPolya-kovZamolodchikov (KPZ) relation between scaling exponents of a conformal eldtheory in a Euclidean planar domain and in quantum gravity, has received a renewedattention from IPhT's researchers. A rst mathematically rigorous proof of the KPZrelation, twenty years after its discovery, has been given, which uses a probabilisticand geometrical notion of quantum area measure. The relation of this new resultwith the original derivation has been claried, using heat kernel and CFT methodsand anomaly consistency arguments.

Critical geometrical models on non uctuating lattices are also of the highestinterest, for a variety of reasons. First, they are relevant to probability theory andto our general understanding of critical phenomena. In this direction, the most im-portant is probably the study of interfaces in two-dimensional critical system, whichhas been pushed forward in 2000 by Schramm's seminal work, leading to an explo-sion of activity and of results concerning the so called stochastic LoewnerSchrammevolution (SLE). Among the open questions in this area which are investigated atIPhT, one can cite the generalization of SLE to non simplyconnected regions andto noncritical systems, the need of concrete physical realizations of SLE, and itslink with two dimensional quantum gravity. Other related progress here includespreliminary study of interfaces with branchings and crossings, such as the domain


walls in the Potts model - we note here that the corresponding work [t11/054] wasrecently awarded the Journal of Physics A Best Paper Prize 2011.

Critical geometrical models are also important for a variety of applications, rang-ing from valence bond descriptions of quantum systems to interacting anyons, col-oring problems, and biopolymers. Important progress has been realized in all theseareas.

Meanwhile, the intimate link between statistical physics of discrete systems andcombinatorics can be used to give a purely combinatorial solution to some statisticalproblem in physics or, conversely, apply physical methods to combinatorial puzzles.This deep interplay is a guiding principle for the activity of the combinatorics groupat IPhT, which takes dierent directions, in addition to the already mentionedprogresses in the area of random surfaces.

A rst line of research concerns variations around the Razumov-Stroganov con-jecture, recently proved by Sportiello and Cantini, relating some highly constrainedenumeration problems (such as fully-packed loops on a square lattice in bijectionwith alternating sign matrices, or tilings of domains in the plane) to the groundstate of some physical integrable model (typically the O(n) dense loop model). Athirty-year old conjecture connecting the alternating sign matrices to the so calleddescending plane partitions has been proved. Another issue involves the Gessel'sconjecture, concerning constrained walks in a subset of a square lattice: a combina-torial formula for a subset of Gessel walks has been given.

The combinatorics of discrete integrable dynamical systems is also under inves-tigation, with connections to newly found mathematical structures such as clusteralgebras (a mathematical version of the theory of everything, with applicationsranging from quiver representations and category theory to algebraic geometry andstring theory, via Teichmüller space geometry), as well as to Bethe Ansatz solu-tions of integrable lattice models or spin chains. For instance, one nds that a classof discrete Hirota-type integrable evolution equations may be solved in terms of(commutative or non-commutative) weighted path models, thereby allowing to provedeep conjectures such as the positivity of certain cluster algebras.

An important area of research and progress pushed forward by IPhT's membersconcerns twodimensional quantum eld theories with supersymmetry, more speci-cally sigma models with supermanifold targets. The study of this topic stems frominterest in the phase transitions of non-interacting disordered electronic systems,such as the transition between plateaux in the integer quantum Hall eect, butsupersigma models also play an important role in the study of geometrical prob-lems like percolation and polymers, as well as in the the GreenSchwartz or purespinor formulation of string theories. These models typically exhibit non-Hermitianhamiltonians, and present considerable diculties in non perturbative analyses. Inparticular, the associated conformal eld theories are logarithmic, and involve notfully reducible representations of the Virasoro and fusion algebras.

The progress in this area has been profound, and due in large part to the solutionof lattice model discretizations of super target sigma models. These discretizationson the one hand have opened the way to using mathematical tools and conceptsdeveloped in the eld of associative algebras in the last ten years, uncovering newrelations between physics and representation theory. On the other hand, the dis-

http://ipht.cea.fr/Docspht/search/article.php?id=t11/054


cretizations, have furthered relations with geometrical models, the lattice analogs ofchiral algebras being in most cases diagram algebras such as the Temperley Lieb orthe Brauer algebras. The interplay between conformal eld theory and loop models(and variants thereof) has thus been particularly fruitful. Major results include thesolution of conformal supersphere and superprojective sigma models, the discoveryof dualities between sigma and Gross Neveu models in the orthosymplectic case, thesolution of the strong coupling CFT associated with θ = π superprojective sigmamodels, and the construction of a general formalism to tackle boundary logarith-mic CFTs using quantum groups at roots of unity. Applications range from edgestate properties in the spin quantum Hall eect to the classication of boundaryconditions for loop models. The latter have also been the subject of very interestingstudies in random matrix theory. Meanwhile of course, geometrical models are anatural tool to dene and tackle new types of eld theories. Recent work on domainwalls and interfaces in the Potts model for instance has yielded promising results formodels with branchings, exhibiting new patterns of exponents and other physicalfeatures, not seen before.

Another instance of quantum eld theory on a curved spacetime is quantum eldtheory in the de Sitter space. In this context more insight has been gained on theintriguing behavior of the particle decay in this spacetime, thanks to the study ofthe KällenLehmann decomposition of the oneloop two point function for a scalartheory.

Another direction of activities in mathematical physics concerns classical andquantum dynamical systems, in clean or noisy systems. On example of classicaldynamics concerns some elementary 1D dynamical systems, the interval exchangetransformations and their generalizations. In spite of the simplicity of their deni-tion, these transformations can lead to subtle ergodic properties, and represent anactive part of the modern mathematical theory of dynamical systems.

Still in 1D, the addition of a multiplicative noise to a simple oscillator can dras-tically modify its long time behaviour; for instance, it can lead to a certain formof intermittency, which is sensitive to the power spectrum of the noise. Such noisydynamical systems can be used to describe as diverse physical phenomena as popu-lation dynamics in a random medium, or the interplay between disorder and nonlin-earity in the 1D Schrödinger equation. The kinematic dynamo problem addressesthe instability of the magnetic eld in the induction equation driven by a givenvelocity eld, neglecting the feedback of the magnetic eld on the ow. In viewof several experimental situations in various conned geometries, the choice of arealistic velocity prole is crucial to determine the threshold for this instability. Asa rst approximation to the situation of a turbulent ow, one can add a stochasticcomponent to the velocity, and observe its eect on the instability threshold .

Various aspects of quantum mechanical systems are also addressed by the mem-bers of our group. One is a random matrix model for decoherence of a spin ina complex environment, obtaining non-Markovian behaviours. More fundamentalquestions in quantum mechanics, namely the interplay between reversibility, localityand causality and their consequences on the quantum formalism are also addressed.The scattering theory for nonlocal potentials is studied, as well as the descriptionof the phenomenon of echoes or antiresonances within the formalism of Regge


trajectories in the complex angular momentum plane. Specic 1-particle scatteringsystems are studied, namely those for which the corresponding classical ow ex-hibits a chaotic set of trapped trajectories; there the focus is on the description ofthe resonances and metastable states in the semiclassical limit. A similar formalism,including the spectral study of a nonselfadjoint Hamiltonian, is used to describethe propagation of damped waves in chaotic domains. Back to 1D, several methods(exact WKB method, ODM method) are used to study the spectra of certain 1Dpolynomial potentials, including non self-adjoint, PT-symmetric cases.

Finally, the zeros of Riemann's zeta function, are used to generate a family ofsecondary zeta functions, which are then carefully analyzed. Although the problemseems purely number theoretic, one should keep in mind that these zeros often serveas a mock spectrum for a quantized chaotic system.

This chapter contains contribution from a number of permanent researchers (M.Bauer, I. Bena, G. Biroli, J Bros, J. Bouttier, F. David, B. Eynard, P. Di Francesco,B. Duplantier, M. Gaudin, M. Grana, E. Guitter, I. Kostov, K. Mallick, R, Minasian,P. Moussa, S. Nonnenmacher, C. Normand, V. Pasquier, R. Schaeer, H. Saleur, D.Serban, P. Vanhove, A. Voros, J. Zinn-Justin) and J. L. Jacobsen, in part-timedelegation from Université Paris-Sud until 2008. The activity of the group wasstrengthen by a relatively large number of post-docs (A. Alexandrov, A. Ayyer,S. El-Showk, A. Gainutdinov, S. Giusto, N. Gromov, M. Guic , N. Halmagyi, K.Hosomichi, J. Manschot, B. Poszgay, F. Saueressig, A. Saxena, B. Vercnocke, B.Vicedo) and of PhD students (R. Bondesan, G. Borot, J.-E. Bourgine, C. Candu,J. Dubail, G. Giecold, E. Goi, O. Marchal, D. Marques, S. Massai, N. Orantin, F.Orsi, A. Puhm, C. Ruef, E. Schenck, I. Shenderovich, R. Vasseur, D. Volin).

The activity of the group was partly nanced by 2 ERC Starting Grants and anumber of ANR projects.


A.1 Flux compactications

Flux compactications remains one of the mainresearch directions of string theory. In spite ofmuch recent progress there is a number of out-standing open problems concerned both with theapplied side, i.e. relations with particle physicsand supersymmetric low energy theories, andconceptual aspects, such as reconciliation withthe string dualities and quantum properties.

A.1.1 Generalized geometry and globalaspects (M. Graña, R. Minasian, N.Halmagyi, D. Márques, E. Goi)

The so-called non-geometric backgrounds doarise when one tries to perform dualities whichhave global obstructions. Ref. [t08/118] focusedon the description of these non-geometric back-grounds from the point of view of generalizedgeometry (a generalized version of Riemanniangeometry that combines the metric and gaugepotentials into larger geometric structures). Alocal generalized geometrical denition of thenon-geometric charges appearing in eectivefour-dimensional theories has been proposed us-ing the Courant bracket and some global as-pects, such as whether the local non-geometriccharges can be gauged away, have been ad-dressed as well. In [t07/134] similar questionshave been addressed from the point of view ofsigma models on target spaces given by a princi-pal torus bration, and it was shown how treat-ing the 2-form B as a gerb connection capturesthe gauging obstructions and the global con-straints on the T-duality. It was shown in partic-ular that the obstruction to T-duality lies in thenon-Hamiltonian action of the symmetry group.Ref. [t08/252] addressed the global issues, suchas quantization of the pure spinors, in topolog-ical theories, and discussed the relation to thetwisted K-theory classication of D-branes.

Ref. [t09/039] gives the description of uxbackgrounds where all the string dualities (per-turbative and non-perturbative) are manifest,using the language of exceptional generalized ge-ometry, an extension of generalized complex ge-ometry appropriate for M-theory backgrounds.The kinetic terms as well as the potential arisingon the four-dimensional eective theory uponcompactication, were encoded in U-duality co-variant expressions. Using this U-duality co-variant formulation, all the possible uxes (ge-ometric and non-geometric) arising in com-pactications have been classied in [t10/093].These uxes correspond to gaugings on the four-dimensional eective theories, and such classi-cation gives the complete dictionary between

four-dimensional gauged supergravities and ten-dimensional string theories.

One of the key phenomenologically attractivefeatures of compactications with uxes is theirpotential to give masses to moduli (unphysicalfour-dimensional massless scalars arising in ux-less compactications, which correspond mostlyto parameters of the internal geometry). In Ref.[t09/328] the set of massless and light elds wereidentied for particular internal coset-type man-ifolds, i.e. it was shown that a truncation of theten-dimensional theory to this subset of modesis consistent. The landscape of supersymmetricand non-supersymmetric vacua (including thepossibility of de Sitter vacua) is explored. Ref.[t11/014] performs a systematic study of sta-bilization of moduli in the presence of U-dualuxes in compactications on toroidal geome-tries, identifying for example regions of param-eter space that do not admit complete modulistabilization.

In [t09/022] discrete families of (ux) back-grounds on internal manifolds of dierenttopologies were constructed by performing cer-tain coordinate dependent O(d,d) transforma-tions. The principal examples of this construc-tion include respectively the family of type IIBcompactications with D5 branes and O5 planeson six-dimensional nilmanifolds, and the het-erotic torsional backgrounds. Classes of non-supersymmetric solutions in toroidal compact-ications were obtained in [t07/135] from thefour-dimensional low-energy theory. One of theinterests of these solutions is that if the StandardModel lives on D-branes in such backgrounds,the supersymmetry breaking is communicatedto the visible sector (the open strings attachedto the D-branes) in the form of soft terms, asexpected in the MSSM. The geometrically in-duced mu-term is computed, and the patternsof soft-terms in each type of breaking are dis-cussed. The eective scalar potential turns outto possess interesting phenomenological proper-ties. Ref. [t10/022] analyzes the conditions forobtaining de Sitter vacua in string theory on theexample of IIA compactications on solvmani-folds with O6/D6 sources. A new treatment ofthe non-supersymmetric source terms was pro-posed. While for space-time lling supersym-metric branes, the energy density is minimizedby a pullback of a special form given by a purespinor, in our solution, the combined bulk-braneenergy density is extremized by replacing theDBI action by a pullback of a polyform fromthe bulk, which is no longer pure.

In [t09/327] a generalization of the Courant













bracket was shown to arise from the Lagrangianfor the two-dimensional sigma model. The cen-tral properties of non-geometric backgrounds areintrinsically stringy and as such it was importantto understand the origins of the target space al-gebraic structures from the string worldsheet.

In [t10/245] the space of BPS solutions of IIsupergravity on the resolved conifold was ana-lyzed. Type II supergravity on conifold back-grounds provided important ways of engineer-ing supergravity duals to four dimensional superYang-Mills theory and as such are important forunderstanding the basic holographic dictionaryaway from the conformal limit. In this work weclassied the BPS solutions for massive IIA su-pergravity and proposed a particular family ofsolutions to be mirror to a previously known so-lution of IIB supergravity on the deformed coni-fold. Particular emphasis was placed on the factthe the space of BPS solutions in the IIB theoryhas an extra branch not seen in the IIA theoryand it was proposed that this missing branch ofIIA solution would be non-geometric in nature.

A.1.2 Instanton eects (F. Saueressig)

Stringy and non-perturbative eects are impor-tant ingredients for building semi-realistic mod-els connecting string theory to four-dimensionallow energy physics. In particular, the instan-ton eects originating from euclidean D- andNS5-branes wrapping submanifolds of the inter-nal space still pose many unanswered questions.A setup where one can hope to understand sucheects in detail is type II string theory com-pactied on a Calabi-Yau threefold (CY). Inthis case, the low energy physics is capturedby a N = 2, d = 4 supergravity action and itis conceivable that the constraints coming fromstring dualities and supersymmetry suce to de-termine the perturbative and non-perturbativecorrections to the low energy eective action.The non-perturbative duality chains underlyingthis program together with the exact expressionencoding the D(-1)- and D1-instanton correc-tions arising in the Type IIB string compacti-cation are summarized in the proceedings arti-cle [t07/136]. By mirror symmetry, these correc-tions are equivalent to the A-Type D2-brane in-stanton corrections arising in the Type IIA com-pactication on the mirror CY.

Determining the full D2-brane instanton cor-rections via electric-magnetic duality requireda detailed understanding of quaternion-Kählermanifolds without toroidal symmetries. This is-sue was addressed in two mathematical works[t08/104] and [t08/115] which developed the

twistor space description for hyper-Kähler andquaternion-Kähler manifolds, respectively. In-stead of working with the rather complicatedmetric of the quaternion-Kähler manifold itself,this formulation encodes all the relevant geomet-rical data in holomorphic transition functionswhich connect the various patches of the twistorspace. As its main virtue this construction ad-mits deformations of the transition functions,which explicitly break the symmetries intrinsicto previous projective superspace constructions.This feature together with the close connectionto wall-crossing formulas made the formalismtailor-made for capturing non-perturbative cor-rections as deformations of the classical transi-tion functions.

The work [t08/203] then developed thetwistor-space description of the A-type D2-instanton corrections, by formulating the pre-viously known results in the language of contactgeometry. Covariantizing the resulting transi-tion functions with respect to electro-magneticduality and employing mirror symmetry, all D-instanton corrections arising within the type IIcompactications were found as a concise sumof dilogarithmic functions. This picture wascompleted by the explicit construction of theD-instanton corrected type IIA and type IIBtwistor spaces in [t09/066] which also led to ex-plicit expressions for the non-perturbative cor-rections to the classical mirror map.

A.2 Heterotic strings (R. Minasian,A. Puhm)

Although the advent of string dualities and uxcompactications has somewhat sidelined het-erotic strings, it has remained an active and im-portant research area due to the appealing fea-tures of the heterotic compactications as well asa number of unresolved fundamental questions.

While it has been known for a long time whatconditions the internal geometry should satisfyin order to preserve supersymmetry in the pres-ence of non-trivial NS H ux, interesting con-structions appeared only recently. Ref. [t10/160]studied the non-linear sigma model realization ofa heterotic vacuum with N = 2 space-time su-persymmetry. In particular the requirements of(0,2) + (0,4) world-sheet supersymmetry havebeen examined and it was shown that a geo-metric vacuum must be described by a principaltwo-torus bundle over a K3 manifold.

In [t08/185] Narain T-duality was consid-ered on a nontrivially bered n-torus bundle inthe presence of a topologically nontrivial NS Hux. The action of the duality group on the










topology and H ux of the corresponding typeII and heterotic string backgrounds was deter-mined. Specializing to the case of supersym-metric T 2-bered torsional string backgroundswith nontrivial H ux, it was proven that thetopology change under the T-duality preservesthe global tadpole condition in the total space aswell as on the base of the torus bration. Someof these T-dualities exchange half of the eldstrength of an unbroken U(1) gauge symmetrywith the anti-self-dual part of the curvature of aphysical circle bration, and it was veried thatsuch T-dualities indeed exchange the supersym-metry condition for the circle bundle with thatof the gauge bundle.

In [t10/159] the heterotic CFT/geometrycorrespondence was studied for non-rational in-ternal conformal eld theories with N=(0,2) su-persymmetry through the triality between min-imal models, Landau-Ginzburg orbifold theo-ries and sigma models on Calabi-Yau manifolds.This was checked using a counting algorithmthat allows to compute the charged masslessspectrum of a wide class of SO(10) GUT mod-els. It was found that while untwisted sectorscan eectively be treated like in (2,2) models, intwisted sectors non-BPS states contribute to thespectrum.

A.3 Black holes in string theory

String theory is a quantum theory of gravity,and has had several astounding successes in de-scribing properties of black holes. The stringtheory group is very active in several areasof black hole physics: constructing and count-ing horizonless black hole microstate geome-tries, obtaining a microscopic description of Kerrblack holes, calculating the moduli-dependanceof black hole degeneracies via wall-crossing, andnding the mechanisms by which string theoryrealizes chronology protection in black hole in-teractions.

A.3.1 Supersymmetric black hole mi-crostate geometries (I. Bena, S.Giusto, C. Ruef)

Recent progress in string theory points tothe possibility that black holes should not bethought of as fundamental objects, but rather asstatistical ensembles of a huge number of smoothgeometries. Establishing this requires the con-struction and counting of very large classes ofsolutions that have the same charges, mass andangular momentum as a black hole, but haveno horizon. The Saclay team has solved severallongstanding and important problems in this di-

rection.The rst is the construction in [t07/075] of

the rst microstate solution corresponding to ave-dimensional black ring that has a macro-scopic horizon. The second is the discovery ofthe so-called abyss solutions [t07/075]. Theseare smooth low-curvature horizonless solutionsthat have a throat whose length can be arbi-trarily large. Since this is not allowed by theAdS-CFT correspondence, it must be that quan-tum eects stop this throat from being arbitrar-ily large, and thus can destroy a macroscopicallylarge chunk of a smooth low-curvature classicalsolution. This phenomenon, conjectured rst in[t07/075], has been conrmed by a rigorous anal-ysis by a team from University of Amsterdam.

In [t08/033] we investigated a transformationthat relates various black hole microstate geome-tries, and that corresponds to spectral ow inthe dual CFT. This transformation can relatesmooth solutions with a multi-center Taub-NUTbase to solutions where one or several Taub-NUT centers is replaced by two-charge super-tubes. Since supertubes can depend on arbitraryfunctions, this established that the moduli spaceof smooth horizonless black hole microstate so-lutions is classically of innite dimension. Thisentropy that comes from a supertube in such abackground was found in [t08/075] to be para-metrically larger than the entropy of a similarsupertube in at space, and this entropy en-hancement mechanism can give entropies of thesame order as the entropy of a black hole, comingentirely from smooth horizonless conguration.

We have also explored the relation betweenthe description of supertubes using their Born-Infeld action (which is a probe approximation),and using the full supergravity solution, andfound that the Born-Infeld description capturesthe same essential physics as the complete super-gravity solution [t08/211]. We have also showedthat the charges that give the enhanced entropyof a supertube can be much larger than theasymptotic charges of the solution containingthe supertube. Last, but not least, we couldshow that all the three-charge black hole mi-crostate geometries constructed so far can beembedded in AdS3 × S3, and hence can be re-lated to states of the D1-D5 CFT.

To fully establish the entropy enhancementmechanism, we constructed the largest knownclass of fully-backreacted black hole microstatesolutions [t10/081], which contain a round su-pertube that has an arbitrary density mode, andhence depend on an arbitrary function of onevariable. When this function is constant these










solutions become usual Denef-type multicenterfour-dimensional solutions [t08/211], but whenthe density is an arbitrary function the four-dimensional interpretation disappears. Since thesolutions found in [t10/081] are much more com-plicated than the ones used to argue that theentropy of smooth supergravity solutions can-not be black-hole-like, our construction reopensthis fascinating question.

A.3.2 Microstates from string theory (S.Giusto)

The need to develop a systematic method to con-struct the geometries representing black hole mi-crostates is the motivation behind the work in[t10/006], where string amplitudes for the emis-sion of closed string states from a D1-D5 boundstate were computed. These amplitudes providethe large distance expansion of the gravity andRR elds emitted by a system of D-branes, andthus link the gravitational and microscopic de-scription of black holes. In [t10/006] the consis-tency of the method was tested by reproducingthe asymptotic expansion of the known 2-chargemicrostates.

A.3.3 Kerr/CFT correspondence (M.Guic )

The (generalized) Kerr/CFT correspondence isa conjectured duality between an extremal rotat-ing black hole and a CFT, whose central chargeis proportional to the angular momentum of theblack hole. If shown to be correct, this dualityprovides an explanation for the microscopic ori-gin of the entropy of all extremal rotating blackholes.

In order to better understand this proposedholographic duality, it is useful to embed specicexamples in string theory. In [t10/247], we havestudied a one-parameter family of extremal non-supersymmetric black hole solutions in super-symmetric compactications of string/M-theoryto ve dimensions. The black holes carried elec-tric graviphoton charge Q and SU(2) angularmomentum JL, obeying Q3 ≤ J2

L. We showedthat in the maximally charged limit Q3 → J2

L,the near-horizon geometry becomes a singularquotient of AdS3×S2, which coincides preciselywith the near-horizon geometry of a black stringsolution to the same theory carrying magnetic

charge P = J13

L .Oftentimes, the microscopic duals of the

black strings are known, and they are CFTswith central charges cL = cR = 6P 3. In thelimit we considered, this central charge agreeswith that of the cL = 6JL CFT predicted by

the Kerr/CFT correspondence. At linear orderaway from maximality, the CFT is in a ther-mal state and we have moreover shown that itsassociated thermal entropy reproduces the lin-early sub-maximal Kerr-Newman entropy. Be-yond linear order, for general Q3 < J2

L, one hasa nite-temperature quotient of a warped defor-mation of the magnetic string geometry. Thecorresponding dual deformation of the magneticstring CFT potentially supplies, for the gen-eral case, the cL = cR = 6JL CFT predictedby Kerr/CFT. Near maximality, the deforma-tion can be studied using the known tools ofAdS3/CFT2.

A.3.4 Background dependence of super-symmetric spectra (J. Manschot)

An important problem is the dependence of thequantum-mechanical spectra of supersymmetrictheories on parameters which encode the shapeof the manifolds (or background) on which thetheory is considered. Part of the spectrumcan become unstable and disappear from thespectrum under variation of these parameters(or vice versa). In supergravity, this part ofthe spectrum corresponds to multi-center blackholes.

Ref. [t10/130] analyses the (stable) spectrumof black hole solutions in N = 2 supergravitywith 3 centers as function of parameters of theCalabi-Yau. The main results are that the par-tition function, which enumerates the number ofsupersymmetric states is convergent, and the re-quirement of so-called rational invariants as ameasure for the number of states. Using theserational invariants, Ref. [t11/080] with B. Pio-line and A. Sen gives an elementary understand-ing using Boltzmann statistics of mathematicalwall-crossing formulas. Ref. [t11/080] also ap-plies localization techniques to determine thenumber of states associated to multi-center blackholes, which in this context means that knowl-edge of collinear black hole solutions is sucient.This idea is made more precise and applied muchmore generally in Ref. [t11/082].

A system whose background dependence isvery similar to that of supergravity, is N =4 Yang-Mills on a complex surface S. Refs.[t10/138] and [t11/078] analyse this system forgauge groups U(2) and U(3) in a more math-ematical setting. Ref. [t10/138] analysed themodular properties and provided an exact for-mula (similar to the Rademacher formula) forthe number of supersymmetric states. Refs.[t11/078] applies [t10/130] and gives the gener-ating function for rank 3; the generating func-
















tions for rank 1 and 2 were derived by Göttsche('90) and Yoshioka ('94) respectively. The pro-ceedings [t11/081] extend this analysis and ad-dress the holomorphic anomaly in this context.

A.3.5 Chronology protection (I. Bena, B.Vercnocke)

One of the most puzzling facts to emerge fromthe study of black holes is the so-called chronol-ogy protection: physical processes cannot cre-ate congurations with closed timelike curves(ctc's). Since the presence of these curves is gov-erned by certain coecients in a given solution,which can easily change by changing charges orangular momenta by a very small amount, it isinteresting to understand why these small ctcinducing changes cannot happen physically.

In [t08/211] we studied the merger of a blackring and a supertube, which for many ranges ofcharges and angular momenta can naively pro-duce black ring solutions that have closed time-like curves. We have found that in the mergersfor which a complete supergravity solution ex-ists (when the supertube and the ring are con-centric), chronology is never violated. However,in mergers where the supertube enters the blackring horizon at some azimuthal angle, in or-der for chronology to be protected the chargesbrought in by a supertube cannot be simply thecharges that appear in its Born-Infeld action,but must depend on the azimuthal angle in anontrivial way. The conrmation of this predic-tion awaits the full supergravity solution for themerger.

In [t10/248] chronology protection was stud-ied from the point of view of the stringy exclu-sion principle. We investigated and proved, us-ing the AdS/CFT correspondence, the one-to-one correspondence between chronology viola-tion/protection in a family of supersymmetricsolutions to AdS supergravity in three dimen-sions and the absence/presence of negative normstates in the spectrum of the dual CFT, throughthe condensation of type IIB 7-branes.

A.3.6 Multicenter non-BPS black holes(I. Bena, S. Giusto, C.Ruef)

It has been known for a few years that instring theory and supergravity there exist a verylarge number of multi-center supersymmetric so-lutions. Although the second-order Einstein'sequations governing these solutions are nonlin-ear, supersymmetry allows one to factorize theseequations into rst order ones, which are rela-tively straightforward to solve. These solutionsgenerically depend on two coordinates, and their

physics has greatly advanced our understandingof supersymmetric black holes.

It has been a longstanding problem to tryto obtain multicenter non-supersymmetric solu-tions, and to see if the interesting physics thatthe supersymmetric solutions have yielded is justan artifact of supersymmetry, or extends to moregeneric black hole congurations that are closerto those of the real world. Nevertheless, in theabsence of supersymmetry solving the second-order nonlinear Einstein's equations to is highlynontrivial, and solutions that depend on twovariables are notoriously dicult to nd. Thebest example of such a solution is the Kerr blackhole, which was found almost 50 years after Ein-stein discovered his equations.

In [t09/020] we have used a certain fac-torization of Einstein's equations (called thealmost-BPS ansatz) for extremal non-BPS so-lutions to construct the rst two-center non-supersymmetric solution that has a nonzero an-gular momentum. We then extended this workand constructed a nonsupersymmetric solutionthat has an arbitrary number of aligned centers[t09/113]. We have also used the almost-BPSansatz to construct the seed solution (fromwhich all other solutions can be generated bydualities) for the most general under-spinningfour-dimensional extremal black hole in stringtheory [t09/020].

Using a similar technology, we have con-structed a class of non-supersymmetric non-extremal solitonic solutions that have the samemass and charges as a nite-temperature blackhole with a macroscopic horizon [t09/130].There are only 2 other classes of such solitonicsolutions known at this point, and their exis-tence and physics supports the fact that the so-called fuzzball proposal applies not only to BPSblack holes, but also to non-BPS nonextremalblack holes.

In [t09/137] we used the fact that somebranes do not feel a force in certain systems(this corresponds to a calibration) to nd anew factorization of Einstein's equations intoa rst-order system of equations that describesnon-supersymmetric multicenter solutions. Wehave found a way to solve these equations lin-early, and have given a recipe to construct11-dimensional and 5-dimensional supergrav-ity solutions using as a base-space any four-dimensional Euclidean electrovac solution to theEinstein-Maxwell equations, and in particular,Israel-Wilson four-dimensional spaces. The so-lution with an Israel-Wilson base interpolate be-tween the BPS and the almost-BPS solutions, to










which they reduce in certain limits.

This construction was extended in [t09/271],where non-BPS solutions were constructed start-ing from arbitrary elecrovac solutions. This pa-per contains the largest known class of smoothve-dimensional non-supersymmetric solutionsdual to microstates of non-BPS nonextremalblack holes, constructed starting from four-dimensional Euclidean Kerr-Newmann-Taub-Bolt solutions.

We have also found in [t11/065] a new non-supersymmetric black ring in Taub-NUT thatunlike all the other known black rings in Taub-NUT has two angular momenta. This black ringsolution has an Israel-Wilson base space, andis completely regular despite being located at apoint where both the metric of the base spaceand the warp factor are singular: the singulari-ties cancel each other to yield a completely phys-ical warped solution.

A.3.7 Solutions in pure gravity (S. Giusto,A. Saxena)

In [t08/297] some recently developed generatingtechniques were applied to the construction ofan exact solution of 5D Einstein gravity rep-resenting a neutral black ring in a Taub-NUTspace. This solution provides the gravitationaldescription of a system of D0 and D6 branes,and the knowledge of the exact solution allowedus to study the interactions between D0 and D6branes and their equilibrium congurations invarious limits, including the extremal limit inwhich the thermal excitations of the D0 branesare turned o.

A.4 Structure of gauge theory andstring theory amplitudes

Gauge theory and quantum gravity amplitudecomputations have recently been a tremendousresearch activity, revealing a surprising connec-tion between amplitudes in quantum gravity,and non-Abelian gauge theories. These connec-tions are between the weakly coupled regimesof these theories whereas the AdS/CFT relationputs in relation a strongly coupled gauge the-ory with a weakly coupled gravitational theoryin curved space. By combining the constrainsfrom unitarity in various dimensions and dual-ity relations in string theory it has been pos-sible to derive a proliferation of new relationsand results for previously unknown or seeminglynot-calculable amplitudes in eld theory, both ingauge theory and supergravity.

A.4.1 Structure of gauge theory ampli-tudes (P. Vanhove)

We have shown that for given tree-level ampli-tudes of in total n incoming and outgoing parti-cles there exists a minimal basis of amplitudes inwhich all other color-ordered amplitudes in QCDcan be expanded [t09/092], [t10/023]. This isan enormous simplication when the number ofparticles grows, and, moreover, we have pro-vided a constructive determination of a mini-mal basis. We showed, as well how to recon-struct generic tree-level amplitudes in gauge andgravity amplitudes from this basis and a mo-mentum kernel function, depending only on thekinematical invariants of the interactions pro-cess [t10/145]. The construction used the con-nection between tree-level gauge theory and gra-vity amplitudes and the zero slope limit of stringtheory amplitude. This form of the tree levelamplitudes points to striking relations betweengauge and gravity amplitudes, that have impor-tant implication at the quantum level [t10/045].By using these relations in the unitarity cuts ofone-loop, we have shown that such a reductionimplies relations between coecients of the one-loop amplitudes when expanded in a basis ofscalar integral functions [t10/030].

The combined action of gauge (dieomor-phism) invariance and maximal supersymmetryimply remarkable simplications in the pertur-bative structure of N = 8 supergravity am-plitudes. We have showed in [t08/018], and[t08/057] that these imply that all n gravitonsone-loop amplitudes can be expressed solely interms of scalar box integral functions in four di-mensions, proving that N = 8 supergravity am-plitude satisfy the no-triangle property. Surpris-ingly we showed [t08/156] that one-loop mul-tiphoton amplitudes with at least eight exter-nal photons, satisfy the no-triangle propertiesin four dimensions as well.

A.4.2 Automorphic properties of stringtheory in various dimensions (P.Vanhove)

In [t10/001], [t10/039] and [t08/100] we anal-ysed the structure of higher-loop interactionsin N = 8 supergravity. Using the constrainsfrom supersymetry and non-perturbative duali-ties we have determined the form of the 1/2, 1/4and 1/8-BPS coupling to the low-energy eec-tive action in dimensions 3 ≤ D ≤ 10 for maxi-mally supersymmetric type II superstring com-pactied on tori. These coupling satisfy non-renormalisation theorems that we have showed,implying the absence of ultraviolet divergences
















for N = 8 supergravity in four dimension un-til seven loops [t10/012]. We showed as wellin this work, that the decoupling limit of mas-sive perturbative and non-perturbative stringstates is singular as a consequence of the non-perturbative dualities.

A.4.3 Perturbative string theory in var-ious dimensions (P. Vanhove, B. Ver-cnocke)

In [t07/126] we have analyzed the structureof the low-energy expansion of one-loop four-graviton amplitude in type II string theory. Wehave showed that the α′ expansion of the an-alytic contribution only involve polynomials indepth one zeta values, and that the integrandcan be expessed in terms of new modular form,now studied by a PhD student of Don Zagier.

In [t09/086] we have determined the com-plete ultraviolet behaviour of four-gluon multi-loop amplitudes in N = 4 super-Yang-Mills indimensions 4 ≤ D ≤ 10 using the pure spinorformalism. We have showed that non-planarcontributions have a milder ultraviolet behav-ior than the leading planar contributions. In[t08/019] a modied prescription for the integra-tion over the pure spinor cone in the functionalintegral was provided, in order to resolve the is-sues in evaluating the D-term type of contribu-tions in amplitudes. An introductory review ofscattering amplitudes in string theory appearsin [t10/177].

A.4.4 Asymptotically safe quantum gra-vity (F. Saueressig)

Weinberg's asymptotic safety conjecture statesthat gravity constitutes a consistent and predic-tive quantum eld theory within Wilson's gen-eralized framework of renormalization. The keyingredient in this scenario is a non-Gaussianxed point of the gravitational renormalizationgroup (RG) ow which controls the UV behav-ior of the theory and ensures the absence of un-physical divergences. Exploring this intriguingpossibility typically relies on functional renor-malization group equations (FRGEs), which en-code the ow of an entire Lagrangian action onthe space of all possible theories. The mainevidence supporting the existence of the xedpoint thereby originates from approximate non-perturbative solutions of the FRGE.

In [t07/154] we constructed a partial dif-ferential equation capturing the RG ow ofmodied gravity theories of the form S =∫ddx√gf(R). Based on this equation we

showed that certain classes of non-local gravi-

tational interactions monomials, including, e.g.,∫ddx√g ln(R) and

∫ddx√gR−n, popular in

cosmological model building, can consistently bedecoupled from the ow and are not generateddynamically. Moreover, expanding the f(R)-equation in positive powers of the scalar curva-ture, it was found that the monomials R3, R4, . . .do not give rise to relevant couplings. This re-sult provided rst hand evidence that the UV-critical surface of the non-Gaussian xed point isactually nite-dimensional, backing up the pre-dictivity of the construction.

Building on these results, [t09/012] carriedout the rst non-perturbative approximation ofthe gravitational RG ow, which included thesquare of the Weyl-tensor as a non-scalar curva-ture term (R2 + C2-approximation). Notably,the gravitational xed point known from thef(R)-computation remained stable in the pres-ence of the new interaction monomial. More-over, from the four coupling constants con-tained in the ansatz only three are associatedwith relevant directions implying an experimen-tally testable prediction of asymptotic safety atthe four-derivative level. In addition it wasdemonstrated that asymptotic safety may beable to cure the sickness of perturbative higher-derivative gravity resulting from the occurrenceof poltergeists. In [t09/024] the R2 + C2-computation was supplemented by a free scalarmatter eld. At the perturbative level, this set-ting constitutes the prototype of a theory whichis perturbatively non-renormalizable at one-looplevel: the C2-interaction is the one-loop coun-terterm arising from the quantization of theEinstein-Hilbert action in the presence of thescalar. Most remarkably, the non-Gaussian xedpoint known from the Einstein-Hilbert plus mat-ter computation, persisted in the presence of theC2-term, leading to the conclusion that asymp-totic safety can also be saved once perturbativecounterterms are included.

A.5 Integrability, AdS/CFT cor-respondence and the exactspectrum of the N = 4 SYMtheory

The most prominent example of AdS/CFT cor-respondence relates the N = 4 super Yang-Millstheory and string theory on AdS5 × S5. In thelast decade, it became clear that, in the planarlimit, the dilatation operator of the N = 4 su-per Yang-Mills theory is equivalent to an inte-grable super-symmetric spin chain. The prob-lem of nding the complete spectrum of anoma-










lous dimensions (or, equivalently, of quantiz-ing the free strings in the AdS5 × S5 back-ground) was therefore reduced to the diagonal-ization of this long-range spin chain. In thelimit of large charges, the spectrum is encodedin a set of Bethe ansatz equations, while for -nite charges the energies are determined by thethermodynamic Bethe ansatz equations, alter-natively written in the form of a so-called Y-system. The validity of the Bethe ansatz equa-tions and that of the Y-system was establishedby extracting the anomalous dimensions for var-ious operators and by comparing them with thepredictions both from the perturbative gaugetheory (weak coupling) and perturbative stringtheory (strong coupling). Among the most stud-ied examples are the twist-two operator, whoseanomalous dimension is related to the so-calledcusp anomalous dimension, also known underthe name of scaling function. On the string side,the corresponding state is associated with thefolded rotating string with angular momentumS in AdS5 and J = 2 in S5. Another testingexample is oered by the Konishi operator, theoperator with the lowest charge whose anoma-lous dimension is not protected by supersymme-try. All the cases studied until now, involvingcomputations up to ve loop order in gauge the-ory and up to two-loop order for strings, conrmthat Bethe ansatz equations and the associatedY-system are able to reproduce exactly both theperturbative gauge theory regime and the per-turbative string regime. The existence of an in-tegrable model which interpolates between thetwo perturbative limits conrms the validity ofthe AdS/CFT conjecture and provides a non-perturbative solution to the spectral problem.

General aspects of integrability, includingthe contributions of the authors and new results,were reviewed in the habilitation thesis [t10/042]and in the PhD theses [t09/286] and [t09/283]which were published as invited review articlesin special numbers of J. Phys A. In [t10/042]the development of the ideas of integrability inthe context of AdS/CFT are reviewed. Specialemphasis is put on the relation with long-rangeintegrable spin chains, the connection with theHubbard model, the strong coupling limit of theBethe ansatz equation. A chapter is devoted tothe thermodynamical Bethe ansatz and the Y-system. In [t09/283] the emphasis is put on theformulation of the integral Bethe Ansatz equa-tions as a Riemann-Hilbert problem. Several ex-amples of such equations are solved perturba-tively by Wiener-Hopf techniques. In [t09/286]the algebraic curve method is reviewed, together

with the method of quantization at one loop pro-posed by the author together with P. Vieira.Various application concern the determinationof the dressing phase at one loop at strong cou-pling (the so-called Hernandez-Lopez dressingphase), as well as the computation of nite-sizecorrections for dierent string solutions.

A.5.1 The BES equation and the scal-ing function (N. Gromov, I. Kostov,D. Serban, D. Volin)

The Bethe ansatz equations determining thecusp anomalous dimension, or the scaling func-tion, were rewritten by Beisert, Eden and Stau-dacher (BES) as an integral equation for themagnon density. While at weak coupling thisequation can be solved straightforwardly orderby order in the coupling constant g, its strongcoupling limit is non-uniform in the spectral pa-rameter and the 1/g expansion is dicult to con-trol. In [t08/007] we have proposed a methodto transform the BES equation determining theanomalous dimension of the twist-two opera-tors into a set of dierence equations obeyed bythe resovent, which are valid for arbitrary cou-pling constant. These equations can be solvedat strong coupling recursively at any order in1/g. It was shown that the analyticity prop-erties satised by the resolvent are sucient tox uniquely the solution and this justied therecursive procedure employed by the Basso, Ko-rchemsky and Kotanski in 2007 to compute thecusp anomalous dimension.

An equation similar to the BES equation,proposed in 2006 by Freyhult, Rej and Stau-dacher (FRS) xes the generalized scaling func-tion. The generalized scaling function controlsthe large S behavior of the dimension of opera-tors with J ∼ lnS. The method of the dierenceequation proposed in [t08/007] was extended tothe FRS equation in [t09/044], and solved to thetwo-loop order at strong coupling. On the otherhand, the two-loop generalized scaling functionwas obtained directly from the Bethe ansatzequations in [t08/094]. Up to a term due to thedierent order of limits implied by the dier-ent procedures, the two results agree. A initialdisagreement with the direct string computationby Roiban and Tseytlin 2007 was subsequentlycorrected by the authors of the string computa-tion. The small J limit was shown by Alday andMaldacena, 2007 to be described by the O(6)sigma model. In [t08/094] the leading logarith-mic terms associated with the O(6) sigma modelwere evaluated for any order in 1/g.

Inspired by the relation between the FRS













equation and the O(6) sigma model put forwardby Basso and Korchemsky in 2008, the methodof the dierence equation was adapted to thegeneric O(N) sigma model in [t09/081]. An an-alytical derivation of the mass gap of the O(N)sigma models was given and the large-order be-havior of the weak coupling asymptotic expan-sion for the energy was investigated. It wasfound that for suciently large N the series issign-oscillating, which is expected from the largeN solution of the sigma model, while for N = 3and N = 4 the series are of constant positivesign.

The BES equation contains a dressing fac-tor which is not determined by the PSU(2, 2|4)symmetry alone, but it is constrained by acrossing-like equation written by Janik in 2006.Beisert, Eden and Staudacher, 2006 wrote downan integral representation for the dressing fac-tor, but a direct verication that this ansatzsatises the crossing equations was lacking. In[t09/079], a constructive proof was given thatthe BES dressing phase is the solution of thecrossing equation with minimal number of sin-gularities.

A.5.2 Semiclassical limit and the alge-braic curve method (N. Gromov, D.Serban, I. Shenderovich, D. Volin)

The semiclassical limit of the non-linear sigmamodel describing strings in AdS5 × S5 can beexpressed in terms of an algebraic curve withPSU(2, 2|4) symmetry. The algebraic curve canalso be obtained by taking the continuum limitof the Beisert-Staudacher equations, and it wasused as a constraint in xing the general struc-ture of these equations. A method to computethe string one-loop corrections by quantizing thealgebraic curve was proposed in 2007 by Gro-mov and Vieira. Unlike the Beisert-Staudacherequations, which neglect wrapping interactionsin the spin chain and therefore miss a part of thenite-size corrections, the quantization of the al-gebraic curve captures the exact nite-size cor-rections at one loop. In [t08/130] a very gen-eral, ecient way to compute the uctuationfrequencies is provided, which allows to deter-mine the energy shift for generic multi-cut so-lutions. The procedure was applied to two-cutsolutions, in particular to the giant magnon so-lution, and allowed to determine the nite-sizecorrections at subleading order. The latter werethen compared to the nite-size corrections fromLüscher-Klassen-Melzer formulas and found tobe in perfect agreement. In [t08/017] the formal-ism was used to compute the leading exponential

correction to the quantum energy of the funda-mental excitation of the light-cone gauged stringin AdS5 × S5, which is the giant magnon solu-tion. Two independent ways to obtain this cor-rection are presented: the rst approach makesuse of the algebraic curve description of the giantmagnon. The second relies on the purely eld-theoretical Lüscher formulas, which depend onthe world-sheet S-matrix. The two approachesagree to all orders in g/∆, where ∆ is the stringenergy.

The method of the algebraic curve was usedin [t11/017] to one-loop quantize the foldedstring solution for the type IIB superstring inAdS5×S5. Explicit results were obtained for ar-bitrary values of its Lorentz spin S and R-chargeJ in terms of integrals of elliptic functions. Theleading three coecients of strong coupling ex-pansion of short operators and in particular theanomalous dimension of the Konishi state wereobtained. Unlike in the case of the scaling func-tion, this series is in half-integer powers of theinverse coupling constant 1/g. The results agreewith the values predicted numerically at inter-mediate coupling from the Y-system approachby Gromov, Kazakov and Vieira in 2009. Thishelped settle a long-standing controversy aboutthe validity of the Y-system results at strongcoupling. The nite size corrections for the largefolded rotating string were also obtained in theform of a series in 1/ lnS. The computation wasdone both in the algebraic curve formalism andusing the Y-system.

The issue of the stability of the semiclassi-cal solutions was addressed in [t08/051]. Highlyspinning classical strings on R×S3 are describedby the Landau-Lifshitz model or equivalently bythe Heisenberg ferromagnet in the thermody-namic limit and their spectrum can be given interms of spectral curves. It is a priori not clearwhether any given admissible spectral curve canactually be realized as a solution to the discreteBethe equations, a property which can be re-ferred to as stability. In order to study the is-sue of stability, the general two-cut solution orelliptic curve was found and explored. It ap-pears that all admissible spectral curves are in-deed stable if the branch cuts are positioned ina suitable, non-trivial fashion.

A.5.3 The AdS4/CFT3 correspondence(N. Gromov)

A new case of AdS/CFT correspondence wasdiscovered recently (O. Aharony, O. Bergman,D. L. Jaeris, and J. Maldacena, 2008), relat-ing the N = 6 super-symmetric Chern-Simons








theory in 2+1 dimensions and string theory inthe AdS4×CP 3 background. This new examplebears many resemblances the with AdS5/CFT4

case, including the fact that the computation ofthe spectrum in the planar limit could also bereduced to the diagonalization of an integrablespin chain. Many of the results which were ob-tained in the AdS5/CFT4 context were trans-posed to this new example. In [t08/128] thealgebraic curve with OSp(2, 2|6) symmetry wasderived. It encodes all classical string solutionsat strong t'Hooft coupling and the full two loopspectrum of long single trace gauge invariant op-erators in the weak coupling regime. This con-struction can also be used to compute the com-plete superstring semi-classical spectrum aroundany classical solution. In [t08/121] a set of Betheequations yielding the full asymptotic spectrumto all orders in the t'Hooft coupling. Theseequations interpolate between the 2-loop Betheansatz of Minahan and Zarembo and the stringalgebraic curve determined by N. Gromov and P.Vieira in [t08/128]. The several SU(2|2) sym-metries of the theory seem to highly constrainthe form of the Bethe equations up to a dress-ing factor whose form was also also conjectured.In [t08/129], the uctuation energies around thealgebraic curve solution for the folded stringwere computed, using the results from [t08/128].A resummation procedure was given, and un-der this procedure the one-loop scaling func-tion computed from the algebraic curve coin-cides with the one computed from the Betheansatz equations proposed in [t08/121].

A.5.4 Classical integrability of the cosetsigma model (B. Vicedo)

The classical integrable structure of Z4-gra-ded supercoset sigma-models, arising in theAdS/CFT correspondence, was studied in[t10/026] and [t09/143]. In [t10/026] the cen-tral object is the standard R-matrix of the Z4-twisted loop algebra. In order to correctly de-scribe the Lax matrix within this formalism, thestandard inner product on this twisted loop al-gebra requires a further twist induced by theZhukovsky map, which also plays a key rolein the AdS/CFT correspondence. The non-ultralocality of the sigma-model can be under-stood as stemming from this latter twist since itleads to a non skew-symmetric R-matrix.

In [t09/143] the Lax connection of the Green-Schwarz superstring in AdS5 × S5 was con-structed within the Hamiltonian formalism. Theresult coincides with that obtained by M. Magroin 2009. It diers in a crucial way from the Bena-

Polchinski-Roiban connection by terms propor-tional to the Hamiltonian constraints. These ex-tra terms ensure that the integrals of motion areall rst class, and that the Lax connection is atin the strong sense.

A.6 Holography and gravity duals(I. Bena, M. Graña, R. Minasian,N. Halmagyi, G. Giecold, F. Orsi,S. Massai)

In the low-energy limit, the gauge/gravity cor-respondence maps a strongly coupled quantumeld theory to a weakly coupled classical gravitytheory. This map has far-reaching consequencesfor understanding the nature of string, gravityand gauge theories. It has led to the discoveryof new important properties of supersymmetricgauge theories (integrability or dualities).

A.6.1 Supersymmetry breaking inAdS/CFT

One of the main open problems remaining intheoretical physics, if we believe in supersym-metry, is understanding how it is broken. It wasshown recently that dynamical supersymmetrybreaking in a long-lived meta-stable vacuum isa phenomenologically viable possibility inN = 1supersymmetric QCD.

For theories with a gravity dual, thegauge/gravity correspondence would be atpresent the tool to study such strongly cou-pled phenomena. Refs. [t09/237] and [t11/019]are the rst steps in a programme developedat IPhT to nding meta-stable vacua in certainN = 1 gauge theories whose supersymmetricvacua are well understood on the dual gravityside.

One such metastable vacuum was conjec-tured by Kachru, Pearson and Verlinde to ariseby placing anti D3-branes in the Klebanov-Strassler dual geometry. In [t09/237] we havehas succeeded in constructing implicitly the non-supersymmetric solution sourced by these anti-D3 branes, by perturbing around the super-symmetric Klebanov-Strassler solution. The 16-dimensional space of perturbations around thesupersymmetric solution at the linearized levelwas solved, and the candidate meta-stable vacuafully identied within the system. The analy-sis has shown that the only solution that couldcorrespond to a metastable anti-D3 brane solu-tion must have a certain singularity in the in-frared. In general such singularities are excludedin string theory, and if this is so in this con-struction, this implies that anti D3 branes mustsource non-normalizable modes, and hence are















not dual to vacua where supersymmetry is bro-ken spontaneously.

If so, this would invalidates the KKLT con-struction of de Sitter vacua in string theory, andwould change completely the way string cosmol-ogy is done. On the other hand, if this singu-larity is acceptable, then we have constructedthe rst-order backreacted solution correspond-ing to the metastable vacuum of the Klebanov-Strassler theory. This solutions would allow oneto nd the vacuum expectation values of manyphysically relevant operators, which would allowone to better use this vacuum for string phe-nomenology and cosmology model-building pur-poses.

This construction was extended to M-theoryputative duals of metastable vacua of 2+1 di-mensional theories, where the supersymmetrybreaking objects are anti-M2-branes, and a sim-ilar but stronger infrared singularity was foundin all candidate metastable solutions [t10/169].

In order to extend the anti-D3 solution to lesssymmetric setups, a consistent supersymmetrictruncation of the ten-dimensional supergravitysystem was identied in [t10/132], which con-tains as a subset the system used in [t09/237].

Besides their gauge theory relevance, the so-lutions with antibranes are also a crucial in-gredient in mechanisms to construct viable cos-mologies within string theory. In [t10/174], thefull analytic form of the attractive potential forD3-branes, (which gives the inaton potentialin these string-cosmology scenarios) was com-puted.

A.6.2 New solutions dual to supersym-metric four-dimensional theories

In [t08/253], a class of super-conformal beta-deformed N = 1 gauge theories dual to stringtheory on AdS5 × X with uxes, where X isa deformed Sasaki-Einstein manifold. The su-pergravity backgrounds are explicit examplesof Generalized Calabi-Yau manifolds: the coneover X admits an integrable generalized com-plex structure in terms of which the BPS sectorof the gauge theory can be described. The mod-uli spaces of the deformed toric N = 1 gaugetheories are studied on a number of examplesand are in agreement with the moduli spaces ofD3 and D5 static and dual giant probes.

New families of interpolating two-parametersolutions of type IIB supergravity were con-structed in [t09/109]. These correspond toD3-D5 systems on non-compact six-dimensionalmanifolds which are T 2 brations over Eguchi-Hanson and multi-center Taub-NUT spaces, re-

spectively. One end of the interpolation corre-sponds to a solution with only D5 branes andvanishing NS three-form ux. A topology chang-ing transition occurs at the other end, wherethe internal space becomes a direct product ofthe four-dimensional surface and the two-torusand the complexied NS-RR three-form ux be-comes imaginary self-dual. Depending on thechoice of the connections on the torus bre, theinterpolating family has either N = 2 or N = 1supersymmetry. In the N = 2 case it can beshown that the solutions are regular.

A.7 Enlarging the scope of theAdS/CFT correspondence

Recently AdS/CFT has found applications farremoved from its original setting in string theoryincluding AdS/QCD, AdS/CMT and entirelynon-string-theoretic models such as Vasiliev gra-vity. This suggests that AdS/CFT, as a tool tostudy strongly coupled theories, has much widerapplicability than initially appreciated.

A.7.1 Fundamental issues (S. El-Showk)

In two dimensions scale invariance combinedwith unitarity (and some other constraints) im-ply conformal invariance. While it is oftennaively thought that this also holds in other di-mensions counter-examples have been known toexperts for some time. In [t11/068] we exam-ine the interesting case of free YM in d 6= 4 andnd that it admits a non-unitary conformal ex-tension given by inclusion of the ghost and anti-ghost eld. More precisely the theory containsa unitary sector (the physical elds) but confor-mal symmetry does not commute with BRST soa physical eld may be a descendent of a ghost.Unfortunately the combination of BRST, anti-BRST and conformal symmetry does not gener-ate a nite dimensional algebra and it is thus notclear that this structure can be extended beyondthe free theory. Interestingly, however, combin-ing only BRST or anti-BRST with conformalsymmetry does generate a closed sub-algebra ofOSp(d, 2|2).

In order to isolate essential features of theAdS/CFT duality, and denude them of theirstringy origins, in [t11/069] we exploit the con-formal bootstrap construction of CFTs to de-termine which (strongly) coupled CFTs mightadmit AdS duals. Constrained only by confor-mal invariance we nd (independently of anyunderlying microscopic model) necessary condi-tions for a sector of the CFT to admit a naturaldescription in terms of a dual bulk theory andcompare our nding to known examples in or-










der to extract the general principles underlyingthe duality. This approach also highlights thequalitatively dierent nature of perturbative andnon-perturbative bulk states in the CFT, withthe former admitting a natural bulk descriptionwhile the latter seem to live most naturally inthe CFT (as they are manifestly holographic).

A.7.2 Stringy corrections (R. Minasian)

Stringy corrections in AdS/CFT generally fallinto the category of either α′ eects or stringloop eects, corresponding to 1/λ and 1/N cor-rections, respectively, in the dual eld theory.While α′3R4 corrections have been well stud-ied, at least in the context of N = 4 super-Yang-Mills, less is known about the 1/N2 cor-rections arising from closed string loops. In[t10/161], AdS5 × X5 compactications of theIIB string were considered, and the closed stringloop correction to the anomaly coecients a andc in the dual eld theory were computed. ForT 1,1 reductions, the string loop correction yieldsc− a = 1/24, which is the contribution to c− aof a free N = 2 hypermultiplet. The paper alsostarted the study of reductions to lower dimen-sional AdS theories as well as the investigation ofthe nature of T-duality with higher derivatives.

A.7.3 New solutions duals to two-dimensional theories (G. Giecold, N.Halmagyi)

In [t09/326] we constructed a family of holo-graphic RG ows from eleven-dimensional su-pergravity on the seven-sphere. An impor-tant technical tool we used was a particulartruncation of maximally supersymmetric SO(8)-gauged supergravity in four dimensions. Thespace of AdS4 solutions within this truncationhave been known for some time but it had beenan outstanding problem to classify the domainwall solutions which interpolate between them.We found new BPS ow solutions which inter-polate between all the BPS critical points in thistruncation and gave a three-dimensional eldtheory interpretation. The generic ow in thisclass preserves just two supercharges and dueto this minimal amount of supersymmetry, thegravity techniques we developed were crucial inunderstanding the phase structure of the eldtheories. A key structure of this family of owsis a certain universality in that the generic owsin this family all terminate at the same point inthe IR, demonstrating that one particular AdS4

solution is an attractive basin in the space ofBPS solutions.

There exists some incertitude in the lit-

erature about the nature of the deconningphase transition in 2+1 dimensional gauge the-ories - whether this transition is rst-order orKosterlitz-Thouless. Given that there existsa Klebanov-Strassler-like supergravity solutiondual to a conning 2+1 dimensional gauge the-ory, we have constructed the black hole solutiondual to the deconned high-temperature phaseof this theory [t09/221], and argued that thephysics of this solution indicates that the phasetransition is not Kosterlitz-Thouless.

A.7.4 AdS/CFT for condensed matterapplications (N. Halmagyi)

With a view towards studying quantum eldtheories of interest to condensed matter physics,we have studied gravitational systems dual toeld theories which are not Lorentz invariant.One crucial issue in applying holographic tech-niques to such eld theories is establishing thatthe gravitational background dual to the groundstate of eld theory is stable. In the work[t10/246] we performed a detailed analysis ofthe spectrum around a particular non-BPS AdS4

background found from eleven-dimensional su-pergravity on the seven-sphere. The back-ground had been proposed in the literature asthe ground state of the rst string embeddingof a so-called holographic super-conductor. Wecomputed a family of modes which violate theBreitenlohner-Freedman bound thus renderingthis solution unstable.

In the work [t11/066] we have used four di-mensional gauged supergravity to classify gra-vity solutions to certain non-relativistic quan-tum eld theories. The eld theories in question,while not possessing Lorentz invariance do pre-serve a particular scaling symmetry. The totalsymmetry groups of these solutions are knownas Schrödinger or Lifshitz symmetries. We foundseveral innite classes of solutions to four dimen-sional gauged supergravity with these symme-tries, some of which are known to admit embed-dings into string theory.

A.8 Topological recursion

In many problems of enumerative geometry, oneis interested in counting geometrical objectswith given topologies. For instance in string the-ory, one wishes to count Riemann surfaces witha given number of handles and given numberof boundaries, with a certain weight. Randommatrices can also be rephrased into the prob-lem of counting discrete surfaces (for instancetriangulations) of given topologies. In many ofthese problems it was found, or sometimes only







observed or conjectured, that there is a univer-sal relationship between counting functions ofdierent topologies. The topological recursionis a recursion which allows to count surfaces ofhigher topologies, in terms of number of surfacesof lower topologies. In some sense it says thatevery surface can be decomposed into a pair ofpants and a lower topology surface (see gure).Eventually, the topological recursion allows tocount objects of all possible topologies, by know-ing only how to count objects with the lowesttopology, i.e. the disc and cylinder. We wrote areview on this subject [t08/189].

A.8.1 Topological recursion and matrixmodels (B. Eynard, N. Orantin, G.Borot, O. Marchal)

Initially, the problem in random matrices, was tond all the coecients of the large size expan-sion of a random matrix problem. It was foundthat those coecients could be computed recur-sively: each new coecients can be computedfrom the previous. Eventually, this shows thatall the coecients are fully determined by theknowledge of the rst one. The rst coecient,called the initial data, or also called the spectralcurve, is not determined by this recursion, it hasto be determined by another method, dependingon the problem under consideration.

This led us to dene, for every initial data(i.e. for any spectral curve), a sequence of co-ecients determined by this recursion. Theyare sometimes called symplectic invariants of thespectral curve. This is a mathematical axiomat-ical denition. Its interest comes from the factthat the sequence of coecients dened this way,have lots of applications in physics and mathe-matics, and also they have many nice geomet-rical properties: rst they are invariant undersymplectic transformations of the spectral curve,whence their name, and they have nice modulartransformations, they obey the so-called specialgeometry, and they encode an integrable system.

Many of our eorts in the past few years fo-cused on studying the mathematical propertiesof the symplectic invariants and topological re-cursion.

For instance in [t09/015], we try to under-stand the integrable structure of those invari-ants, and we show that they satisfy some de-terminantal formulae, which are typical of inte-grable systems. In [t08/164] we study the mod-ular properties of those invariants, and we showthat they transform in a way opposite to θfunctions. This shows, that if we multiply themby a θfunction, we get some modular invariants.

In [t09/196], we try to understand the ge-ometric origin of the topological recursion. Insome sense, the symplectic invariants shouldcount some number of surfaces living in a cer-tain space, and obeying certain symmetry prop-erties (although it is not so clear which space andwhich symmetry properties in general). The re-cursion consists in observing that a surface canbe cut into pieces, and thus the number of sur-faces can be obtained by adding and multiply-ing the numbers of elementary pieces, this iswhat the topological recursion does. Imaginethat we can start from one boundary (which hasthe shape of a circle) of the surface, and propa-gate it at constant velocity parallel to itself intothe surface. At the beginning, the boundary isa circle, and sweeps a cylinder. But necessar-ily, at some time, the boundary cannot remaina circle, it gets pinched. We cut the surface atthat time, and remove the cylinder swept. Theremaining piece of the surface has in general asmaller topology, and thus we get a recursionon the topology of the surfaces we count (seeg.A.1).

In [t11/045], we found a new formula, ex-pressing the symplectic invariants, in terms ofcounting Riemann surfaces with a weight givenby some topological characteristic classes. Thisleads to associate to any spectral curve a certaincharacteristic class in the moduli space of Rie-mann surfaces. This characteristic class is verysimply computed as the Laplace transform ofthe spectral curve. The implications of that for-mula are still to be understood. We could showso far, that the formula introduced in [t11/045]reproduces famous formulae as special cases,for instance the famous ELSV (EkedahlLandoShapiroVainshtein) formula (in other words,the characteristic class of the Lambert spectralcurve is the Hodge class), or the MariñoVafaformula (the characteristic class of the framedvertex spectral curve is the product of 3 Hodgeclasses) are special cases of it. This formula alsoshows that mirror symmetry is very closely re-lated to Laplace transform.

A.8.2 CFT approach to matrix models(I. Kostov, N. Orantin)

The CFT description of the matrix models[t98/112] can be used to obtain in a closed formthe genus expansion of the observables. The sad-dle point of a large N matrix integral denes acomplex curve. In [t10/283] the genus expansionis obtained in terms of a CFT associated withthis curve. To each branch point of the Rie-mann surface one associates an operator which









Figure A.1: Topological recursion: we start from one boundary (which has the shape of a circle)of the surface, and propagate it at constant velocity parallel to itself into the surface. At thebeginning, the boundary is a circle, and sweeps a cylinder. But necessarily, at some time, theboundary cannot remain a circle, it gets pinched. We cut the surface at that time, and remove thecylinder swept. The remaining piece of the surface has in general a smaller topology, and thus weget a recursion on the topology of the surfaces we count.

represents a twist eld dressed by the modes ofthe twisted boson. The partition function of thematrix model is computed as a correlation func-tion of such dressed twist elds. The methodis tested on the simplest example of the Hermi-tian matrix model, where the classical solutionis described by a hyperelliptic Riemann surface.

Another powerful method to compute thegenus expansion is the topological recursion,which also can be formulated entirely in terms ofthe complex curve. It is interesting and impor-tant to understand the relation between the twomethods. It is shown [t10/125] that althoughthe two approaches lead to dierent graph ex-pansions for the higher genus terms, the nalresults are identical. Moreover, the diagramsof the CFT approach can be obtained by as-sembling graphs from the graph expansion thatstems from the topological recursion.

A.8.3 Quantization of Riemann surfaces(B. Eynard, N. Orantin, G. Borot, O.Marchal)

The random matrix model which is solved bythe topological recursion, is a model of a ran-dom matrix which possesses the hermitian sym-metry. Other ensembles of matrices can be de-ned with other symmetries. They are oftencalled Wigner's ensembles classied by a num-ber β, which is β = 1 for hermitian symmetry,β = 2 for symplectic symmetry, and β = 1/2 fororthogonal symmetry, but it can be dened forevery other values of β.

The method which led to the topological re-cursion for β = 1, can be extended to everyvalue of β, with very little changes [t09/175],[t10/154]. In fact, the topological recursion it-self doesn't change, which shows that it is a veryuniversal object. The only thing which changesis the initial data, the spectral curve.

For β = 1, the spectral curve is a curve in the(x, y) plane, it is usually given by an equationf(x, y) = 0 for a certain analytical function f ,

and the ingredients involved in the formulationof the topological recursion, are geometric prop-erties of that curve: the notion of genus, cycles,matrix of periods, holomorphic and meromor-phic forms, formcycle duality, Riemann bilinearidentity, all of them introduced more than 150years ago by Riemann and the other founders ofthe Riemannian geometry of surfaces.

For β 6= 1, we see that the topological re-cursion doesn't change, provided that we rede-ne all those geometric notions. The spectralcurve can still be written with a function f(x, y)but now x and y are some quantum variables,they don't commute, they satisfy yx − xy = ~where ~ is proportional to β−1. If we appropri-ately redene the notions of genus, cycles, ma-trix of periods, holomorphic and meromorphicforms, we nd that the topological recursion isunchanged. Also, with those denitions, all thenice properties of Riemannian geometry remainunchanged, like the Riemann bilinear identity,or the formcycle duality. This allows to denein a very natural way, a quantum Riemanniangeometry of surfaces. Moreover, unexpectedly,we found that the very denition of those ge-ometrical object, implies a Bethe ansatz as aconsistency condition. In some sense, the Betheansatz is the condition that the integral of a dif-ferential meromorphic form along a cycle, de-pends only on the homology class of the cycle,and not on the precise locus of the cycle on thesurface. The Bethe ansatz is the condition thatcohomology is well dened. This is what we doin [t09/175, t10/154]. The consequences of thatgeometry are still under exploration.

A.8.4 Topological recursion, algebraicgeometry and topological strings(B. Eynard, A. Alexandrov, N. Oran-tin, G. Borot, O. Marchal)

An important application of the topological re-cursion concerns algebraic geometry and topo-logical string theory.







+

=

Figure A.2: An example of the correspondence between the graph expansions in the topologicalrecursion and CFT approaches.

Topological string theory, is the low energylimit of string theory, where all the strings are insome sense frozen to their lowest possible energystates, but there can be many such lowest states,which can not be deformed into oneanother,because the compactication CalabiYau spacehas a non-trivial topology.

In string theory in general, one is interestedin counting in how many ways a string can prop-agate from a given initial state to a given nalstate. Topological string theory thus consistsin counting, up to conformal deformations, howmany surfaces with given boundaries and topol-ogy, can be embedded in a target space. Thisnumber is usually an integer, or in fact a ratio-nal number because surfaces with symmetriesare counted quotiented by their symmetry or-der, and is called Gromov-Witten invariants bymathematicians in algebraic geometry.

In 2007, it was conjectured by M. Mariñoand al (BKMP conjecture), that, if the targetspace has an additional toric symmetry, thenits GromovWitten invariants should satisfy thetopological recursion. They checked this conjec-ture on many examples, but a full general proofis still missing and has become an importantchallenge among algebraic geometers. Only veryfew cases, involving the simplest target spaces,have been proved. This would be an importantfact, since this would allow an explicit computa-tion of those invariants.

In [t07/104], we proved that the GromovWitten invariants of a point (the simplest pos-sible target space) indeed satisfy the topolog-ical recursion. This was not the rst proof,but it was the rst one using matrix mod-els. In [t09/055] and [t09/101], we were therst to prove the next simplest case, called theBouchard-Mariño conjecture. In [t09/055], weused a matrix model, and in [t09/101], we pro-

vided a direct algebraic proof, using the so calledcut and join equations. Later, another caseof the BKMP conjecture, for the target spaceC3, was proved independently by Chen, andZhou, using the same ideas we had introducedin [t09/101]. Since then, we found another muchsimpler proof for C3 in [t11/045], using onlybasic algebraic manipulations, and the alreadyproved case of the point. We hope that the ideasintroduced in [t11/045] will allow to prove theconjecture for more complicated geometries.

Beside, we made another attempt to provethe BKMP conjecture for general target spaces,using a matrix model. In [t10/029], we showedthat GromovWitten invariants can be formu-lated as a random matrix problem. This hadbeen long expected in principle since the famousworks of Dijkgraaf and Vafa, and here we exhib-ited an explicit matrix model, which works forevery geometry, i.e. every toric 3-dimensionalCalabiYau space. This matrix model does sat-isfy the topological recursion, but the dicultyin proving the BKMP conjecture, was to iden-tify the initial data of the recursion, i.e. thespectral curve. In order to prove the BKMP con-jecture, one has to prove that the spectral curvearising from the matrix model, is the same asthe spectral curve conjectured by BKMP, whichis the mirror of the target space, issued frommirror symmetry. The matrix model's spectralcurve can be computed as the curve which ex-tremizes the matrix model's energy. In [t10/099]we proved that the mirror curve is indeed anextremum of the matrix model's energy, whichconrms BKMP conjecture. Unfortunately, thematrix model's energy can have many other lo-cal extrema, and we couldn't prove that the mir-ror curve is indeed the absolute extremum, wecould only prove that it is one among possiblelocal extrema, and thus our computation is not












Spectralcurve

density ofeigenvalues

a a j+1,ij,i

!!

j,ij+1,i

Figure A.3: The GromovWitten invariants can be computed by the topological vertex formula,i.e. by counting 3d partitions, glued along the edges of a graph encoding the geometry of thetarget space. The eigenvalues of the matrix model are the positions of boxes across horizontalslices (i.e. cutting vertical edges). The matrix model's spectral curve is the analytical continuationof the limiting density of those eigenvalues in the large size limit. It is thus a surface made ofseveral sheets (each sheet is represented by a horizontal cylinder, there are as many sheets as thenumber of horizontal slices of the graph), glued along cuts (represented by vertical cylinders). Italso has poles corresponding to the frozen boxes (accumulations of poles are represented by greystrips). Thanks to the symplectic invariance property of the topological recursion, the poles don'tcontribute, and can be ignored. After subtracting the poles, the spectral curve is an algebraiccurve, which can be seen as the thickening of the graph, known as the mirror curve.

yet a mathematical proof of BKMP.

In [t08/164], we use the symplectic invariantsdened from the topological recursion, to pro-pose a candidate for the full nonperturbativetopological string partition function. The mainreason for our proposal, is that it is modu-lar invariant (which we prove in [t08/164]). Intopological strings, Bersahdsky, Cecotti, Ooguriand Vafa have found the famous holomorhicanomaly equation, which says that the pertur-bative part of the string theory partition func-tion is not modular invariant, but modular in-variance can be recovered by adding some nonanalytical terms. This was not fully satisfactory,because, according to the expected duality be-tween string theory and conformal eld theory(AdS/CFT correspondence), the partition func-tion should be analytical. We show in [t08/164],

that modular invariance can also be restorednonperturbatively without breaking analytic-ity. Our partition function also has the back-ground property invariance (a perturbative ex-pansion can only be dened near a background,but string theory should eventually be indepen-dent of the choice of background), and satisesmany properties expected for a string theory.

Finally, in [t11/134], we consider another ap-plication of the topological recursion to knot the-ory. Gopakumar and Vafa suggested that the in-variants (Homy colored polynomials) of a knotcan be computed in terms of topological stringsin a certain target space. In [t11/134], we showthat the topological recursion can also apply toknot theory. Starting from the ChernSimonsmatrix models, we can write a matrix modelto compute the knot invariants of torus knots







(knots which can be drawn on a torus). Ourcomputation proves that the spectral curve as-sociated to a torus knot is a symplectic trans-formation of the unknot, thus conrming theGopakumar-Vafa hypothesis.

A.9 Random matrices

Random matrix theory is interested in the statis-tics of eigenvalues of a random matrix, particu-larly in the limit of large random matrices. Theleading order has been known since the pioneer-ing works of Wigner, Dyson and Mehta. Oneof the questions we address is understanding thesubleading corrections to those laws, to all or-ders. Other subjects of research concern therelation between matrix models and tau func-tions and integrability, as well as the relationwith quantum gravity in two dimensions and therelation with non-critical string theory.

A.9.1 Large random matrices (M. Ber-gère, G. Borot, P. Desrosiers, B. Ey-nard, O. Marchal, N. Orantin)

In [t08/026], we show how to compute the largesize expansion to all subleading orders for var-ious matrix models with hermitian symmetry,including the so-called one-matrix and multi-matrix models. We show that to all orders in thesize, there are quasi-periodic oscillations, and wecompute them exactly to all orders. Those oscil-lations are due to some tunneling eects describ-ing eigenvalues jumping from one region withlarge probability to another.

We have generalized the results known formatrices with Hermitian symmetry to othersymmetries. In [t09/163] we compute the largesize expansion of super-matrices containing botha bosonic and a fermionic part. We show thatthe large N expansion is again given by the sametopological recursion as for hermitian symme-try, and in some sense super-matrices are justan analytical continuation of ordinary hermi-tian matrices, except that fermionic eigenvaluesare counted with a negative multiplicity. Thisalso leads to an interesting supersymmetry for-mula which exchanges the roles of bosonic andfermionic variables.

Another ensemble of random matrices whichwas studied is the so-called βensemble de-

scribed in section (A.8.3). The hermitian sym-metry β = 1 has a selfdual property, which al-lows to integrate over the angular part very eas-ily. But for other values of β, there is no ecientknown formula to compute integrals over angu-lar parts of random matrices. In [t08/081] wend some new recursion relations among angularintegrals, and we nd some new formulae whichwe hope could lead to a better understandingof those cases. Our observation is that in the n-dimensional space, when n−1 vectors are chosenorthogonal, then there is only one possibility ofchosing the nth vector so that it is orthogonalto the other n− 1. This gives a relationship be-tween the angular part of matrices of dimensionn and n− 1.

In [t10/154], [t09/175], [t08/140] we nd asystematic way to compute the large size expan-sion of the statistical distribution of eigenvaluesof all β one-matrix ensembles. The method is ageneralization of the topological recursion, andyields a bonus.

The probability distribution of the largesteigenvalue of a random matrix is universal; itis the same for every random matrix model (un-der reasonable assumptions) and it depends onlyon the symmetry group. This probability dis-tribution is called the Tracy-Widom law. In[t10/137], [t10/166], [t10/187] we compute theasymptotic expansion of the Tracy-Widom lawfor all β symmetry groups and we relate it to thetopological recursion; in other words we providea geometric interpretation to the Tracy-Widomlaw.

It has been long observed and conjecturedthat theWigner's ensemble β and 4/β are closelyrelated. This duality is carefully proved in[t08/013] using relations among Jack polynomi-als, and using a matrix Fourier transform.

A.9.2 Matrix models and tau functions(A. Alexandrov, O. Marchal)

Random partitions is a popular subject of mod-ern mathematical physics. They appear in suchdiverse areas as 2d Yang-Mills and 3d Chern-Simons theory, instanton calculus of supersym-metric gauge theories in dierent dimensionsand Hurwitz-Hodge-Gromov-Witten theory. Ofcourse, sums over partitions/representations












play an increasing role in string theory, so allaforementioned theories can be described byparticular string models. In [t10/074] we deriveexact matrix integral representations for dier-ent sums over partitions. The characteristic fea-ture of all obtained matrix models is the pres-ence of logarithmic (or, vice versa, exponential)terms in the potential. The Toda lattice inte-grability of the basic sums over partitions canbe easily derived from the matrix model repre-sentation.

Since the early nineties, when the spectacu-lar Witten conjecture was proved by Kontsevich,the Kontsevich-Witten tau-function, that is thepartition function of two-dimensional topologi-cal gravity, became an inevitable part of math-ematical physics. In [t10/146] we constructeda simple cut-and-join operator representationfor the Kontsevich-Witten tau-function. Ourderivation is based on the Virasoro constraints.Possible applications of the obtained representa-tion are discussed.

Hurwitz numbers count the ramied cover-ings of a Riemann surface. Their calculation isobviously important in string theory and fromtime to time it attracts certain attention. In[t11/100] we have investigated integrable prop-erties of dierent generating functions of gen-eralized Hurwitz numbers. The functions withsimple integrability of Toda and KP type aresingled out.

There exist many denitions of a tau func-tion and integrable system. One of them, isthe notion of isomonodromic tau function, in-troduced by Miwa-Jimbo, which associates a taufunction to a linear system of dierential equa-tions, based on the WKB asymptotics. Thedenition of Miwa-Jimbo applies only to non-degenerate systems (when the eigenvalues of thelimitting system are all distinct). But the so-called 2-matrix model (introduced for instancein order to study the Ising model on a randomlattice)is degenerate. In [t08/196], in collabo-ration with M. Bertola, a generalization of theJimbo-Miwa construction was proposed in orderto prove that the 2-matrix model is indeed anisomonodromic tau function.

A.9.3 Scattering of folded strings in two-dimensional Minkowski space (I.Kostov)

According to a conjecture, advanced by Mal-dacena and based on the matrix model for theEuclidean black hole, the Lorentzian black holemetric is generated by condensation of longfolded strings. Maldacena showed that the re-

ection of a long folded string from the Liou-ville potential is given by the boundary two-point function function in a certain limit. Theamplitude for a state containing two long foldedstrings to come from and go back to innity iscomputed in [t07/188]. The computation is doneboth in the worldsheet theory and in the dualmatrix model, the matrix quantum mechanics.The matrix model description allows to evalu-ate the amplitudes involving any number of longstrings, which are given by the mixed trace core-lators in an eective two-matrix model.

A.9.4 The Student ensemble of corre-lation matrices: eigenvalue spec-trum and Kullback-Leibler en-tropy (G. Biroli)

In collaboration with J.-P. Bouchaud and M-Potters and motivated by the analysis of nan-cial data we studied in [t08/027] a new ensem-ble of random correlation matrices related tomultivariate Student (or more generally ellip-tic) random variables. We established the ex-act density of states of empirical correlation ma-trices that generalizes the Marcenko-Pastur re-sult. The comparison between the theoreticaldensity of states in the Student case and em-pirical nancial data is surprisingly good, evenif we were still able to detect systematic de-viations. Finally, we computed explicitely theKullback-Leibler entropies of empirical Studentmatrices, which are found to be independent ofthe true correlation matrix, as in the Gaussiancase. We provide numerically exact values forthese Kullback-Leibler entropies.

A.10 Random geometries

Statistical models can be considered not only onlattices which are regular, but also on randomlattices with a xed topology (they can be drawnon a surface, for example a plane, a sphere, atorus, etc.). They were initially introduced inconnection with quantum gravity, but they ap-pear now in various problems in physics, rangingfrom string theory to crystal growth, or in biol-ogy to describe uctuating membranes.

The Ising model on a random surface, intro-duced by Kazakov in 1986, is the simplest modelof gravity coupled to matter. Another examplestudied is the O(n) model, introduced by Kostovin 1988, which is a model of self-avoiding loopson a random lattice. This model was used tostudy boundary critical phenomena in randomgeometry. One possible formulation of the sta-tistical models on random graphs is in terms ofrandom matrices, since the Feynman graphs for








matrix integrals generate random surfaces of ar-bitrary topology. Another formulation, of com-binatorial nature, is given in terms of randommaps.

Statistical models can be also considered onrandom trees. Random trees arise in manybranches of science, ranging from the social sci-ences through biology, physics and computer sci-ence to pure mathematics. In physics, randomtrees often occur in the context of statistical me-chanics or quantum eld theory, and fall into oneuniversality class, called generic random trees.Another large class of random trees arises ingrowth processes (for instance branched polymergrowing in a solution), and in many importantreal world cases one can observe the structure ofthe growing tree but only guess the rules whichgovern the growth (social networks, the internet,citation networks, etc.).

A.10.1 Statistical models on random lat-tices (M. Bergère, G. Borot, B. Ey-nard, N. Orantin, A. Prats-Ferrer)

In [t07/118], we compute the probability of Isingmodel congurations with xed given spin signson the boundaries of the surface, with an arbi-trary number of boundaries, and an arbitrarytopology.

In [t08/072], we compute the probabilities forany topologies of another statistical model calledchain of matrices, which is an extension of theIsing model where spins can have L dierent val-ues from 1 to L, and can randomly change byunit jumps. We prove that those probabilitiesare computed by the topological recursion.

In [t09/160], we study another statisticalmodel called O(n) model. We found a methodto compute the probability of such random loopsin various congurations, in all topologies. Thecomputation of probabilities on the plane werealready known, and in [t09/160] we computethem in all other topologies, and the answer isagain given by the same topological recursion al-ready found in many other models. This showsthat the topological recursion is a very universaltool. We conjecture that many other statisticalmodels are also solved by the same topologicalrecursion, for instance the Potts model.

It is also particularly interesting to studywhat happens for very large lattices. Physicistshave understood in the 80's that the limit oflarge lattices is described by a conformal eldtheory coupled to gravity, but this is still notyet considered proved to the mathematics com-munity. In [t09/015], [t09/116], we establish rig-orously some of the results implied by conformal

eld theory.Another interesting problem in statistical

physics concerns crystal meltings, also called 3Dpartitions. The problem consists in randomlypiling cubic boxes in the corner of a room, andask what is the typical surface, in the limit of alarge room with a large number of boxes. Thetypical shape was described in the famous worksof Okounkov in 2003, but what about uctua-tions around the typical shape?

In [t08/056], [t09/050], we show that thisproblem can be mapped to a random matrixmodel, We show how the statistics of the eigen-values of a random matrix, are related to thestatistics of the height of the cubes in the room.This allows to prove that corrections to the typi-cal shape, to all orders in powers of the size of theroom, are computed by the topological recur-sion. This also gives an explanation of why thestatistical behaviors observed in crystal meltingare the same as the universal laws of randommatrices.

A.10.2 Geometrical critical phenomena,matrix models and 2D gravity(J.-E. Bourgine, K. Hosomichi, I.K.Kostov)

The boundary critical phenomena appear in alarge number of elds, ranging from solid statephysics to string theory. The situation becomesmore interesting when the degrees of freedomon the boundary have less symmetry than thosein the bulk. In this case one speaks of surfaceanisotropy. The most studied example of suchboundary behavior are the D-branes in stringtheory. Another example is given by the ferro-magnets with surface anisotropy, which can havea rich pattern of surface transitions. A good lab-oratory for studying such phenomena is theO(n)loop model with −2 < n < 2. In the loop gasformulation of the anisotropic boundary condi-tions, the boundary conditions are introducedby changing the Boltzmann weights of the loopsthat touch the boundary [t06/155]. The prob-lem was formulated on a uctuating lattice in[t07/036]. An exact solution was obtained forthe dense phase of the loop gas. The interpreta-tion of the solution based on the boundary 2Dquantum gravity conrms the spectrum of theboundary operators conjectured in [t09/186].A matrix model formulation of the anisotropicboundary conditions was presented in [t08/193].It was shown that in the rational points of theO(n) model the anisotropic boundary condi-tions correspond to alternating height bound-ary conditions in the RSOS models. The bound-












Figure A.4: A 3D partition, is a piling of boxes in the corner of a room (the room itself may havecorners). It is also a model for crystal melting. When the number of boxes is large, one observesa limit shape separating a liquid region from a frozen region. The limit shape was found byKenyon-Okounkov and Sheeld in 2003. Here, we recover the limit shape using a matrix model,and we also nd all corrections to the limit shape, as an asymptotic expansion in the size of thedomain.

Figure A.5: A loop conguration for the O(n) loop gas with anisotropic boundary conditions. Theloops that touch the boundary (in blue and green) have fugacities n1 or n2 depending on theircolor (n1 + n2 = n).

ary correlation functions involving two dierentanisotropic boundary conditions were computedin [t09/041].

The solution for the dilute phase of the loopgas was obtained in [t09/186] using the corre-spondence with a matrix model. In this, morecomplicated, case the boundary coupling con-stants should be tuned to obtained a conformalboundary condition. The key result is the ana-lytic expression for the boundary two-point cor-relator for any value of the bulk and bound-ary coupling constants. The solution leadsto the same boundary phase diagram and theboundary critical exponents as those obtainedin [t09/073]. Moreover, the solution allows tostudy the bulk and the boundary deformationsaway from the anisotropic special transitions. Inparticular it shows how the anisotropic specialboundary conditions are deformed by the bulkthermal ow towards the dense phase.

A.10.3 Distance statistics in randommaps (J. Bouttier, E. Guitter)

Discrete models for uctuating surfaces appearin various domains of physics, ranging from thestudy of biological membranes to string theory.

Such discrete random surfaces correspond tocombinatorial structures called maps, which arethe subject of an active eld of research withdeep algebraic and probabilistic aspects. Alge-braic aspects arise when one addresses the fun-damental problem of enumeration: how manymaps (i.e. of given size or topology) do exist?Probabilistic aspects are related to rened ques-tions about the geometry of random maps.

The enumeration problem has a long history,starting with Tutte's seminal series of papers inthe 1960's, and punctuated with decisive contri-butions from physicists, namely matrix integralsand related methods.

In [t10/258], we present an introduction tothese methods aimed at both physicists andcombinatorists. The resulting counting formu-las often take a remarkably simple form: this ledpeople to look for alternate elementary deriva-tions of these formulas, which are found in theform of bijections between maps and suitabletrees. It was then realized that these bijectionsgive access to further geometrical information onmaps.

From the random geometry point of view,a natural observable is the graph distance. A






salient question is the existence of scaling limitsfor the distance in large random maps, whichshould then correspond to models of continu-ous random surfaces. Of particular interest isthe so-called Brownian map which describes thegeneric scaling limit of random planar maps inthe universality class of so-called pure gravity,like maps with prescribed face degrees, for in-stance planar triangulations or planar quadran-gulations. The Brownian map was shown tohave the topology of the two-dimensional spherebut it has nevertheless a number of surprisinggeometrical properties, which place it half-waybetween a tree-like object and a smooth surface.A number of these properties were discoveredand characterized quantitatively in the last fouryears by computing a number of laws for thedistance statistics in maps.

Our analysis of the distance statistics inmaps relies on three steps: (1) the aforemen-tionned bijective coding of the maps by deco-rated trees, the so-called mobiles; (2) the ex-act derivation of a number of mobile generat-ing functions, thanks to some underlying inte-grable structure; (3) and nally the analysis ofthe hereby obtained map enumeration resultsin the scaling limit of large maps and prop-erly scaled distances. In [t07/163], attentionis paid to the statistics of geodesics in maps.There it is shown that all the geodesics con-necting two given points on the map remainclose to each other so that they become iden-tical in the scaling limit. This generic propertyfails however for a few exceptional endpointswhich can be linked by (at most three) truly dis-tinct geodesics. The distance-dependent distri-bution of these exceptional points was obtained.The most advanced result in the eld of dis-tance statistics is the computation in [t08/078]of the distance-dependent three-point functionof planar maps, which gives the joint law forthe distances between three random points onthe map. A remarkable phenomenon of conu-ence of geodesics was discovered, which statesthat, in the scaling limit, the two geodesic pathsleading from two arbitrary points to a giventhird one merge into a common geodesic be-fore reaching this point. A precise quantitativestudy of the shape of geodesic triangles can befound in [t08/182] (see Figs.A.6 and A.7). Thephenomenon of conuence reveals some under-lying tree-like structure of the Brownian map.Heuristically, it was claimed that large maps canbe viewed as made of a large component, themother universe with attached small compo-nents, the baby universes arranged into tree-

like structures. This picture is made more pre-cise in [t10/020] where we explore the geometryof minimal neck baby universes (minbus) andderive a number of distance-dependent charac-terizations of these minbus (distance-dependenttwo-point function inside a minbu, law for thedistance from a random point to the mother uni-verse, etc).

All the results above deal with maps hav-ing the topology of the sphere but several ex-tensions were obtained for more involved ge-ometries. In [t09/138], we consider mapswith a boundary and give explicit formulasfor the bulk-boundary and boundary-boundarydistance-dependent correlators in various en-countered scaling regimes (small, dense or criti-cal boundary). The critical boundary regime ischaracterized by a one-parameter family of scal-ing functions interpolating between the Brown-ian map and the Brownian Continuum RandomTree. We also address the question of the bulk-loop distance statistics in the context of mapsequipped with a self-avoiding loop. Another nat-ural extension consists in having maps of highergenus. A rst characterization of their geometryis given in [t10/024] where a number of distance-dependent universal scaling functions are com-puted exactly, characterizing the distance statis-tics of large toroidal maps (probability distribu-tion of the length of the shortest non-contractibleloop passing via a random point - law for the dis-tance between two random points).

Finally, in [t10/135], we return to the dis-crete setting and provide a novel viewpoint onthe integrable structure at work in step (2)above. We show that the basic geometric observ-able, the distance-dependent two-point function,appears within the continued fraction expansionof the simplest global quantity, namely thegenerating function for maps with a boundary.This unexpected connection to the fundamentalproblem of map enumeration explains combina-torially the existence of general exact formulasfor the two-point function.

A.10.4 Random tree growth by vertexsplitting (F. David)

Motivated by our previous study of tree growthmodels by attachment processes (together withP. Di Francesco, E. Guitter, IPhT, and T. Jons-son, University of Iceland), and by our proposalof tree growth models for RNA folding, we haveintroduced and studied a new and general classof tree growth models by splitting and attach-ment processes ([t08/135], work with M. Dukes,T. Jonsson and S. Stefansson from the Univer-










v3

1v 2v

δ3

δ1

δ2

D’31

D’23

D’12

Figure A.6: A schematic picture of the phenomenon of conuence of geodesics in the Brownianmap: if v1, v2 and v3 are typical random points, the geodesics connecting them pairwise havecommon parts of non-zero length δ1, δ2 and δ3. A geodesic triangle is thus characterized by atotal of six lengths, whose law can be computed explicitly [t08/182].

0

0.25

0.5

0.75

10

0.25

0.5

0.75

1

0

1

2

3

0

0.25

0.5

0.75

1

0

2

4

0

2

4

0

0.05

0.1

0.15

0.2

0

2

4

0

0.5

1

1.5

20

0.5

1

1.5

2

0

0.2

0.4

0.6

0

0.5

1

1.5

2

(a) (b)

(c)

δ2

δ1

D12θ( , | )

δ

1

δ2

δ2

δ1

D12θ( , | )

δ

1

δ2

δ2

δ1

D12θ( , | )

δ1

δ2

Figure A.7: Plots of the conditional probability density for (δ1,δ2) given the value of D12 =D′12 + δ1 + δ2 (see notations in Fig.A.6), here for (a) D12 = 1.0, (b) 2.0 and (c) 5.0.

sity of Iceland). This class of models is a vastgeneralisation (with some simplications) of theRNA model of [t07/068], such that at each timestep the tree is separated into two componentsby splitting a vertex and then connecting thetwo pieces by inserting a new link between thedaughter vertices. Besides its interest for ourphysical questions, this model generalises alsogrowth and fragmentation models considered inthe mathematical litterature, such as the prefer-ential attachment model and Ford's alpha-modelfor phylogenetic trees (in particular generaliza-tions of Aldous models). A mean eld theory asbeen developed for the vertex degree distribu-tion. It is proven that this mean eld theory isexact (no uctuation corrections) in some spe-cial cases. The predictions of mean eld theoryhave been checked to agree with extensive nu-merical simulations in general. Exact results areobtained for various correlation functions andmass distribution functions. In particular ex-

plicit formulas are given for the intrinsic Haus-dor dimension of the tree. It is shown thatthis dimension can vary from one to innity, de-pending on the parameters of the growth process(splitting rates) for the model.

A.11 Liouville quantum gravityand KPZ

There is a close relationship between the behav-ior of critical systems in random geometries andthat on regular lattice, discovered by Knizhnik,Polyakov and Zamolodchikov (KPZ). This rela-tionship involves quantum gravity in two dimen-sions, which can be seen in terms of a confor-mal eld theory with a component describingthe matter degrees of freedom, and a Liouvillecomponent, which takes into account the uctu-ations of the underlying lattice. The KPZ re-lation links the critical exponents in the xedand the uctuation geometries. Renewed inter-est to this subject comes from the relation of




Schramm-Loewner evolution (SLE) with confor-mal eld theory and quantum gravity. In thiscontext, it became possible to derive results al-ready known to physicists in a mathematicallyrigorous way.

A.11.1 Rigorous proof of the KPZ rela-tion (B. Duplantier)

(Critical) Liouville quantum gravity is a wayto produce a random geometry from thetwo-dimensional Gaussian (massless) free eld(GFF). One replaces the Euclidean area mea-sure dz on a smooth planar domain D with arandom measure µγ = eγh(z)dz, where γ ∈ [0, 2)is a xed constant and h is an instance of thezero or free boundary GFF on D. Since h isnot dened as a function but as a distributionon D, one has to use a regularization procedure:in the joint work [t08/047] with Scott Sheeld(MIT), the quantum area measure µγ is con-structed as the limit µγ = limε→0 µγ,ε of the reg-ularized quantities µγ,ε := εγ

2/2eγhε(z)dz, wherehε(z) is the mean value of h on the circle of ra-dius ε centered at z. One interprets µγ as thearea measure of a random surface S := (D,h)conformally parameterized by D (Fig.A.8). Aquantum boundary length measure on bound-ary arcs of D is similarly constructed.

Consider now planar d-dimensional fractalsets and the scaling properties of their Euclideanor analogously quantum measures: • If onerescales the domain D via the map z → bz,b ∈ C (so that its Euclidean area is multipliedby |b|2) then the d-dimensional Euclidean frac-tal measure of a fractal X ⊂ D is multiplied by|b|d = |b|2−2x, where x (the so-called Euclideanscaling weight) is dened by d := 2 − 2x(≤ 2).• If X is a fractal subset of a random surface S,and one rescales S so that its µγ-quantum areaincreases by a factor of |b|2, then the quantumfractal measure of X is multiplied by |b|2−2∆,where ∆ is the analogous quantum scaling weight(Fig. A.8).

The celebrated Knizhnik-Polyakov-Zamo-lodchikov (KPZ) relation (1988) then states thatx and ∆ are related by x =

(1− γ2/4

)∆ +

γ2∆2/4.

Twenty years after its discovery, the article[t08/047] with S. Sheeld gives the rst rigor-ous proof of the KPZ relation. We also proveits extension to the boundary case. It rests inparticular on the following Brownian property ofthe GFF: for xed z, the circle average hε(z) isstandard Brownian motion in time t := − log ε.Owing to the use of the regularized conformalfactor eγhε(z) in µγ,ε in constructing the Liou-

ville measure µγ above, this allows seeing theKPZ relation as being in essence a Brownianexponential martingale property. This in addi-tion places the KPZ formula in a much broadercontext than the original conformal eld the-ory (CFT) approach: it is valid for any frac-tal set sampled independently of the Gaussianfree eld, and for any γ < 2 chosen indepen-dently from the fractal, in contrast with the ini-tial KPZ scheme where γ = γ(c) is xed by thevalue of the central charge c associated with thecritical fractal considered. The complete proba-bilistic proof of KPZ requires working with thelimit measure µγ (or its boundary analog) andis given in the mathematical article [t08/047];the essentials for physics are given in the Letter[t09/033] with S. Sheeld, and developed in theLes Houches Seminar lecture [t09/290] and theICMP09 plenary lecture [t09/291].

Another issue is the denition of Liouvillequantum gravity for γ > 2. In the usual CFTapproach γ(c) ≤ 2 with c ≤ 1. The answeris given by duality. The corresponding randomsurface is a treelike foam of Liouville quantumbubbles of dual parameter γ′ = 4/γ, γ < 2,(baby universes) connected to each other atpinch points and rooted at a principal bub-ble parameterized by the domain D. As an-ticiped by Klebanov in 1992, a non-standardKPZ relation exists for γ > 2, which is dual tothe usual relation. A probabilistic derivation ofthis dual KPZ relation is given in [t09/033], us-ing the same Brownian perspective on the GFF(see also the two extended lectures [t09/290] and[t09/291]). A complete proof requires construct-ing the quantum area limit measure for γ > 2.

A.11.2 Derivation of the geometricalKPZ relations (M. Bauer, F. David)

Motivated by the recent derivation by B. Du-plantier and S. Sheeld of the KPZ relationsby probabilistic methods in a 2D geometric set-ting [t08/047], we have studied in [t08/159] therelation between this approach and the originalderivation of the KPZ relations (by conformaleld theory methods) in 2D quantum gravity.Indeed the new formulation applies when com-paring the dimensions of fractal (deterministicor random) sets in a random measure given byan (a priori given) exponential of a free eld the-ory (Liouville theory), while the old one appliesto correlations functions of some CFT in a ran-dom Riemannian metric, and provides a justi-cation of the Liouville theory as an eective eldtheory. In particular their domain of applicabil-ity are in fact somehow dierent (but overlap-













Figure A.8: A quantum gravity dyadic decomposition of the torus, where all Euclidean squareshave similar small quantum areas δ. A random fractal X (here a self-avoiding walk) intersectsthese quantum squares with a probability scaling as δ∆.

ping).We have given a derivation of the geometrical

KPZ relations, by heat kernel and CFT meth-ods, and using anomaly consistency arguments.This approach provides a covariant way (w.r.t.the dieomorphisms) to dene neighborhoods offractals in 2D quantum gravity, via a quantumdiusion process. This shows that both formula-tions of the KPZ relations can be incorporated ina common general framework, within the realmof conformal eld theory.

A.11.3 SLE, KPZ and Liouville quantumgravity (B. Duplantier)

Schramm-Loewner evolution (SLE) is a sto-chastic process, depending on a real parame-ter κ, which describes the universal continu-ous scaling limit of 2D critical curves such as,e.g., percolation (κ = 6), self-avoiding walks(κ = 8/3) and Ising model interfaces (κ = 3).Its invention by Schramm in 1999 is on parwith Wiener's 1923 mathematical constructionof universal continuous Brownian motion. Criti-cal phenomena in the plane (including SLE) arewell-known to be related to conformal eld the-ory (CFT), a fact anticipated in the so-calledCoulomb gas approach to critical 2D statisticalmodels. Liouville quantum gravity, itself a CFT,can be heuristically coupled to other CFT's viaKPZ, and this has been used to predict proper-ties of critical curves and SLE.

However, in the joint work [t10/223] with S.Sheeld, we provide the rst rigorous connec-tion between SLE and Liouville quantum gra-vity. We show that when two boundary arcsof a Liouville quantum gravity random sur-

face are conformally welded to each other (ina quantum length-preserving way) the result-ing interface is an SLE (Fig. A.9). In par-ticular, this rigorously establishes the relationbetween Liouville and SLE parameters: γ =√κ for κ ≤ 4 and γ = 4/

√κ for κ > 4.

This corresponds precisely to the famous rela-tion between the Liouville parameter and thecentral charge in the Liouville-CFT correspon-dence, γ(c) =

(√25− c−

√1− c

)/√

6 ≤ 2 withc = 1

4 (6−κ)(6− 16/κ) ≤ 1. A second dual solu-tion is found as γ′ = 4/γ > 2, which correspondsto the non-standard Liouville quantum gravitymentioned in section A.11.1 above, where thequantum measure develops atoms with localizedarea.

We also develop in [t10/223] a theory ofquantum fractal measures (consistent with theKPZ relation) and analyze their evolution un-der conformal welding via the introduction of ex-plicit SLE related exponential martingales; thelatter play the (now mathematically rigorous)role of the so-called quantum gravity dressingof conformal operators in a CFT coupled to Li-ouville gravity. As an application, we constructquantum length and boundary intersection mea-sures on the SLE curve itself. This for instanceallows calculating the SLE quantum length con-tained in any domain D (Fig. A.9).

A.12 Geometrical models and ap-plications

Statistical models in two dimensions can bedened not only in terms of local Boltzmannweights, but also in terms of non-local objects,which are loops, clusters, interfaces or walls. In




t ( )z

ft

ft ( )0

h ( )z~

ft ( )

f

D

D

w=

( )

tηη h

~( )w

00x’ x

x

Figure A.9: Conformal welding map ft: the quantum gravity boundary lengths associated withthe GFF γh are equal for any pair of real segments [0, x] and [x′, 0] such that ft(x) = ft(x

′), andthe zipped-up curve ηt is an SLEκ with κ = γ2.

particular, this point of view oers a fruitful con-nection with SLE and with fractal properties ofvarious statistical mechanics objects.

A.12.1 Interfaces in 2D statistical me-chanics (M. Bauer, D. Bernard)

Since Schramm's breakthrough in 2000, thestudy of interfaces in two-dimensional criticalsystem has been a very active eld, leading tofruitful contacts between probabilists and con-formal eld theorists. Many results that wouldhave been considered as out of reach before2000 are now elementary exercises in stochasticcalculus exploiting the Schramm-Loewner equa-tion. A celebrated example is Schramm's for-mula. Suppose that due to boundary conditionsan interface in a critical system connects twoboundary points of a simply connected regionand take a point in the bulk. Schramm's for-mula, which gives the probability that the pointin the bulk lies on the left or on the right ofthe interface, can be derived on a single sheet ofpaper.

However, as usual after a rapid progress, newdeep questions have arisen for which there is noclue yet. In such cases, one has to rely on spe-cial properties of particular models to get somehints on a possible general structure.

Among the open questions, we shall stressthree. As we shall see, they are somehow re-lated. The rst is the generalization of SLE tonon-simply connected regions. The second is theinterpretation of SLE in terms of concrete mod-els. The third is the generalization of SLE tonon-critical systems.

Non simply connected regions have moduli.The simplest illustration is a region with thetopology of an annulus. Such a region is con-formally equivalent to a region limited by twoconcentric circles, one with radius one and theother with radius R > 1, and R is the moduli inthat case: two regions with a dierent R are con-formally inequivalent. Non simply connected do-

mains do not have so many symmetries. Annuli,for instance, have only rigid rotations. Most ofthe time, there are no symmetries at all.To contrast with the simply connected case, re-member that Riemann's theorem asserts thatany two simply connected regions are confor-mally equivalent and moreover that these re-gions have enough symmetries to allow either3 boundaries points or 1 bulk and 1 boundarypoint to be chosen at convenience. The rstcase is relevant for chordal SLE (an interfaceconnecting two boundary points) or dipolar SLE(an interface connecting a boundary point to aboundary segment) while the second case is rel-evant for radial SLE (an interface connecting aboundary point to a bulk point). Schramm usedRiemann's theorem to show that conformally in-variant measures on random curves in simplyconnected regions depend on a single parame-ter, denoted by κ.The arguments used by Schramm to derive SLEin simply connected regions are insucient fornon simply connected regions. The best one cando at the moment is to use peculiar propertiesof certain models to x the ambiguities left bygeneral arguments. These peculiar propertiesalso turn out to make it possible to computeexplicitly some features encoded in the relevantSchramm-Loewner equation.For instance, the level lines of the Gaussian freeeld are known to be related to SLEκ=4. In[t10/056] we have shown how this relation al-lows to dene chordal SLE4 processes in an-nuli, describing traces that are anchored on oneof the two boundary components. The precisenature of the processes depends on the confor-mally invariant boundary conditions imposed onthe second boundary component. Extensionsof Schramm's formula to doubly connected do-mains are given for the standard Dirichlet andNeumann conditions and a relation to rst-exitproblems for Brownian bridges is established.For the free eld compactied at the self-dual



radius, the extended symmetry leads to a classof conformally invariant boundary conditionsparametrized by elements of SU(2). It is shownhow to extend SLE4 to this setting. This allowsfor a derivation of new passage probabilities àla Schramm that interpolate continuously fromDirichlet to Neumann boundary conditions.

Turning to the second theme, to oversimplifya little bit, one can say that the interpretationof chordal SLE in terms of statistical mechan-ics models is rather good. The interpretation ofradial SLE is already less clear, but the worstcase is dipolar SLE. To take only one example,we note that SLEκ=8/3 is believed to describeself avoiding walks. This can be supported bynumerics for the chordal and radial cases, butthe meaning of the boundary conditions at theend of the hitting segment for dipolar SLE8/3 interms of self avoiding walks is totally unknown.Recall that dipolar SLE describes interfaces thatjoin a boundary point to a boundary arc in asimply connected region. The central questionanalyzed in [t08/152] is the following: what isthe eect on an interface in dipolar SLE whenit is conditioned to hit a certain sub-arc of theinitial selected boundary arc. This question israther natural if one aims at understanding bet-ter dipolar SLE. We obtained a complete de-scription of the corresponding interface measure,via several tricks, both from the probabilistic ap-proach and from the conformal eld theory ap-proach. We could show that SLEκ=2, which de-scribes the continuum limits of loop erased ran-dom walks, is characterized as being the onlycase for which dipolar SLE conditioned to stopon an interval coincides with dipolar SLE onthat interval. We illustrated this property bycomputing a new bulk passage probability fordipolar SLE2. This characterization should becompared to the analogous characterization ofSLE8/3, which is the only case for which chordalSLE conditioned to avoid a hull is chordal SLEin the region obtained by cutting the hull fromthe initial region.

Looking at interfaces out of the critical pointis also a natural question. Let L be the typicalsize of the system and a be the lattice spacing.When the correlation length is nite in termsof a, the description is not two complicated andhas been understood some time ago. Oversim-plifying again, there is an average position of theinterface, whose length is of order L, the uc-tuations are transverse and of order L1/2, theyare typically of the random walk type with shortrange correlations. When L is sent to +∞, there

is a Brownian continuum limit if the transversedirection is rescaled appropriately.The case when the correlation length is a nitefraction of L, and a is sent to 0, is much morecomplicated. Conformal invariance is lost, andthe interface measures in dierent simply con-nected regions are not related by pure kinemat-ics, as is the case at the critical point. However,for a given domain, say the upper-half plane ora strip, it is still possible to describe the inter-face via a (chordal or dipolar) Loewner evolu-tion. As usual, this evolution involves a ran-dom source term. For SLE, this random sourceterm is a Brownian motion (with a scale

√κ to

be precise). But out of the critical point thestatistics of this random source term becomesextremely complicated. One of the issues iswhether perturbation theory around the criticalmeasure will apply or not. Of course, formally itdoes as shown by a naive eld theory represen-tation where the deviation to the critical tem-perature is obtained by perturbing with an ap-propriate operator. In probability theory, suchperturbations are related to would-be martin-gales, which cannot be computed or even char-acterized explicitly for general κ. When the per-turbed theory is a free eld theory, the situationis much better. This was used in [t07/204] and[t09/132] for κ = 2 and κ = 4. The rst casedescribes loop-erased random walks in the dipo-lar geometry when the underlying random walkis penalized by its number of steps. The eldtheory is that of massive symplectic fermions.The second case describes level lines of the mas-sive Gaussian free eld in the chordal geome-try. One is led to an implicit description of themartingale deforming the interface measure interms of certain functional determinants. Theyinvolve space-dependent mass terms that are akind of substitute for a dependence upon confor-mal transformations. In the loop-erased randomwalk case, a hitting probability can be computedexplicitly for constant mass, allowing to retrievethe statistics of the Loewner source term from anindependent perspective. In the case of κ = 4 wecould show that the statistics of the full Gaus-sian eld factorizes as a product of the statisticsof the interface and the statistics of the Gaus-sian free eld in each of the regions delimited bythe interface.

A.12.2 Multifractal harmonic measureand winding of random 2D inter-faces (B. Duplantier)

In [t08/044], the multifractal behaviour of con-formally invariant curves in two dimensions is






revisited with I.A. Binder (Toronto). The mixedmultifractal spectrum associated with both theharmonic measure and winding (monodromy)near such critical curves, originally obtained viaquantum gravity methods with the same co-author in 2002 [t02/124], is here rederived byCoulomb gas-CFT methods only. The resultsalso extend to the general case of multiple pathsin a star conguration. Consider a random con-formal path S, part of a critical scaling curvein a 2D statistical system, e.g., the trace of aSchramm-Loewner evolution (SLE) (Fig. A.10).

The harmonic measure ω(z) of a ball cen-tered on the path and passing through a pointz is the probability that a Brownian motionstarted away from the path S rst hits S insidethat ball. Electrostatically, one can consider Sas an equipotential, and dene ω(z) as the por-tion of electric charge induced on S inside theball and the winding ϑ(z) as the rotation angleof the Green line (i.e., electrostatic eld line)reaching z from innity.

To extract the asymptotic geometrical har-monic measure and rotation properties of ran-dom paths, we resort to a Coulomb gas for-malism that generalizes that by Bettelheim etal. in 2006. We introduce chiral vertex op-erators, with dierent holomorphic and anti-holomorphic parts, and perform the analysisof their short-distance scaling and monodromyproperties in operator product expansions withpath-creating operators. Their CFT transfor-mation rules under the uniformizing Riemannmap w(z) of the complex plane slit by the ran-dom path(s) yield the desired information aboutthe harmonic measure ω(z) and rotation ϑ(z),via their local correspondence to the conformalmap's derivative w′(z), namely ω(z) ∼ |zw′(z)|and ϑ(z) ∼ − argw′(z). The multifractal mo-ments ωn(z)e−p ϑ(z) for arbitrary powers n andp are thus found to typically scale as |z|x(n,p) forz → 0, with explicit exponents x(n, p). By dou-ble Legendre transform they give access to themixed multifractal spectrum f(α, λ), i.e., to thefractal dimension of the subset of points on thepath where the typical behavior of the complexquantity ω(z)eiϑ(z) is |z|α+iλ for z → 0. Thisis also generalized to multiple random paths ina star conguration, where the harmonic mea-sure and winding exhibit multiple multifractalbehaviours in the various sectors of the confor-mally invariant star. Together with our pre-vious approach via quantum gravity [t02/124],this provides two dierent derivations of thesemultifractal spectra. A third, mathematicallyrigorous, proof has been obtained by the same

authors by working directly with the Schramm-Loewner evolution, and will be the subject of aforthcoming publication.

A.12.3 Domain walls and interfaces -again (J. Dubail, J.L. Jacobsen, H.Saleur)

While most of the activity in the eld hasconcentrated on geometrical loop models, thereare many other situations of interest, involvingbranchings and intersections, whose descriptioneither in terms of eld theory or in terms of SLEis more complicated, or even unknown to thisday. An old example of this was the arborealgas which was found in [t05/025] to be describedby a supersphere sigma model and an eectivenon compact target at criticality. In the last fewyears, we proposed a solution of what is probablythe simplest problem in this family, the statis-tics of domain walls in the Q-state Potts model([t11/054] and [t11/055]). This solution involvesin particular a clean denition of the concept ofdomain walls (which can be thin or thick) forQ generic, and gives rise to exponents in the Kactable which had not been seen before in a geo-metrical setting, raising the challenge for a directeld theoretic understanding. This will proba-bly require a thorough algebraic reformulation,generalizing in particular the Temperley Lieb al-gebra to a new object which encodes both physi-cal spin clusters and Fortuin Kasteleyn clusters.

A.12.4 Boundary loop models (J. Dubail,J.L. Jacobsen, H. Saleur)

While loop models have been by now very wellstudied in the bulk, their properties near theboundary present a wealth of behaviors whichhad been largely unnoticed until quite recently.In a series of works dating back to [t06/155], Ja-cobsen and Saleur discovered in this context newtypes of conformal boundary conditions (dubbednow JS) using ideas from the eld of associativealgebras (boundary Temperley Lieb or blob al-gebras [t94/188]). These boundary conditionswere later studied formally in the context ofmatrix models, but they also oer more con-crete applications. In [t09/281] for instance, thespecial transition in the two dimensional O(n)model with coupling anisotropy breaking thesymmetry down to O(n1)×O(n− n1) was thussolved, and the full phase diagram mapped out.Another application to the coloring problem byJacobsen and Saleur where a dierent number ofcolors in the bulk and the boundary are allowedwas discussed in [t09/068].






z

z

0

θ( )

Figure A.10: A random conformal path S ; ω(z) is the harmonic measure in the ball centered at0 ∈ S and passing through z ; ϑ(z) is the (possibly indenite) winding angle of the Green linereaching the ball when z → 0.

a.

b.

Figure A.11: The two dierent types of DW, here shown in the bulk case (geometry of the inniteplane). A thin DW corresponds to the interface between two clusters of dierent colours (a), whilefor a thick DW the two clusters have the same colour. An illustration for the Q = 3 Potts modelis given (left) as well as a schematic picture for non-integer Q (right).

A.12.5 Valence bonds and entanglement(J.L. Jacobsen, H. Saleur)

Loop models and loop diagrams are also relatedto quantum spin problems via the concept ofvalence bonds. This is particularly useful inthe analysis of entanglement in disordered sys-tems as discussed for instance by Koo, Haas andSaleur in [t07/143]. It also provides a conve-nient intuitive grasp of entanglement in general,by relating it with various statistical features ofvalence bonds connecting subsystems. The va-lence bond entanglement entropy in the XXXspin chain for instance was studied numericallyin details, and found to be remarkably similarnumerically to the usual Von Neumann entan-glement entropy. In [t08/109], Jacobsen and Sa-leur solved in closed form the problem of valencebond entropy for the ground state of the XXZspin chain, and showed that it did in fact behave

dierently (albeit not by much for the isotropiccase) from the Von Neumann result. The re-sulting combinatorial problem exhibits as oftenremarkable properties.

A.12.6 Interacting anyons (Y. Ikhlef, J.L.Jacobsen, H. Saleur)

Temperley Lieb algebras have been revisited inthe recent past in the context of topologicalquantum computers and anyons. It has been ar-gued in particular that hamiltonians expressedin terms of Temperley Lieb generators describedinteracting anyons, and their critical propertiescould be related with occurrences of non abelianstatistics. In [t09/072], we revisited the phasediagram of the anyonic spin chains, and, us-ing in particular geometrical representations andearlier results on the antiferromagnetic Pottsmodel, demonstrated the existence of a new inte-





grable point, described by a new conformal eldtheory they solved independently in [t09/282].While challenged for two years, our claim is nowaccepted in the literature, and should lead to abetter understanding of certain plateaux in thefractional quantum Hall eect.

A.12.7 Random tilings (J.L. Jacobsen)

Although many models of random tilings of theplane have been solved in the past, new ex-amples keep being motivated by applications inphysics and mathematics. In a recent experi-ment by M.O. Blunt et al., a two-dimensionalmolecular network of para-terphenyl-3,5,3',5'-tetracorboxylic acid was adsorbed onto graphite.The rod-like molecules arrange as a dimer cov-ering of the hexagonal latticea priori a well-known tiling problem. However, the experimen-tally measured value of the stiness constantin the corresponding Gaussian free eld theoryturns out to be 1.66±0.08 times larger than thetheoretical prediction. In [t09/336] we have re-lated this eect to an interaction between neigh-bouring dimers of the same spatial orientation.They showed how to map the interacting tilingproblem to a Coulomb gas model and derivedthe corresponding critical exponents. In partic-ular, they predicted that a Kosterlitz-Thoulesstransition would be observed if the experimen-tal compound could be cooled to a temperatureT ' 110K.

A.12.8 Lattice models of biopolymers(J.L. Jacobsen)

Lattice models of loops, and Hamiltonian walksin particular, have often been proposed as toymodels of globular proteins. In [t08/306] weproposed an ecient algorithm providing unbi-ased sampling of three-dimensional Hamiltonianwalks, based on earlier work by Manseld. Inparticular the universal scaling function for theend-to-end distance was obtained with great ac-curacy. In [t10/277] we generalised the algo-rithm to study two walks of equal length thatjointly ll the cubic lattice. As in [t08/306]strong evidence for the ergodicity of the algo-rithm was provided by a companion enumerativestudy [t07/228].

The issue of polymer mixing has recentlygained renewed interest in the area of physicalbiology. One outstanding question is to under-stand the organisation and segregation of chro-mosomes within simple bacteria, including dur-ing duplication. In these applications one typi-cally has two polymer chains conned to a bar-shaped geometry, akin to that of a rod-shaped

cell. In [t10/277] we have given convincing nu-merical evidence that if each chain is modelledby a Hamiltonian walk, the two chains will seg-regate spatially.

A.12.9 Colouring and ow problems(J.L. Jacobsen)

Graphs colourings and related problems have along history at the fronteer between mathemat-ics, computer science, and theoretical physics.The number of colourings can be expressed asthe so-called chromatic polynomial, which oc-curs as the zero-temperature limit of the an-tiferromagnetic Potts model. Computing thispolynomial is #P-hard, meaning that the com-putational eort grows exponentially in the sizeof the graph. In [t10/276] we described anew type of algorithm for computing the chro-matic polynomial of a planar graph. It com-bines the transfer matrix principle with a graph-theoretical construction known as tree decompo-sition. Roughly speaking, this means that timeevolves recursively instead of linearly. The algo-rithm improves the running time from exp(cN)to exp(cNα) with an exponent α which is ' 0.3on average and it is 1/2 in the worst case.

The chromatic polynomial on the triangularlattice was shown to be an integrable model byBaxter (1986). In [t10/278] we have found a79-term series expansions for the bulk, surfaceand corner free energies in the non-critical phase.These series permitted him to conjecture exactproduct formulae for the surface and corner en-ergies for the rst time.

For planar graphs, proper vertex Q-colou-rings are dual to nowhere-zero integer Q-ows,but this equivalence breaks down for non-planargraphs. In [t10/279] in collaboration with Salaswe studied the ow polynomial on a certainclass of non-planar graphs. In 1954 W.T. Tutteconjectured that any (bridgeless) graphs has aQ = 5 ow. A main result of [t10/279] is thatthis conjecture is almost false: there existsgraphs whose ow polynomial has real roots ar-bitrarily close to Q = 5. On a deeper level,[t10/279] demonstrates the relevance of repre-sentation theory in the study of the Q-statePotts model in dimensions higher than two.

A.13 Loop models, integrabilityand combinatorics

The relationship between statistical physics andcombinatorics has undergone tremendous de-velopments in the recent years. Beyond merecounting of congurations, both ideas and tech-niques of statistical physics have been success-














fully applied to solving notoriously hard com-binatorial problems. Loop models with quan-tum symmetries have provided a new frame-work relating standard combinatorial objectssuch as plane partitions and alternating sign ma-trices. Integrability gives new ways of think-ing about combinatorial problems, that involveother branches of mathematics as well, such asprobability theory, algebraic geometry and rep-resentation theory.

A.13.1 Loop gas, combinatorics, andquantum algebra (P. Di Francesco)

As part of a long-standing collaboration withP. Zinn-Justin (LPTHE, Jussieu), we havebeen studying two-dimensional statistical lat-tice models known as loop gases which maybe viewed as contour maps of some random 3Dlandscape. One main motivation was to betterunderstand the rationale behind the Razumov-Stroganov conjecture (2001), identifying a sur-prising connection between probabilities of con-gurations of two loop models in very dierentgeometries.

Some aspects of this relation have been thesubject of intense work from the combinatorialcommunity. This correspondence is indeed re-lated to the so-called Alternating Sign Matrixconjecture, proved independently in the mid 90sby Zeilberger and Kuperberg, and establishingthe identity between the total number of (i) Al-ternating Sign Matrices (ASMs) of size n × n,namely matrices with entries 0, 1,−1 such that±1 alternate along rows and columns, possiblyseparated by any number of 0s, and with rowand column sums all equal to 1 and (ii) To-tally Symmetric Self-Complementary Plane Par-titions (TSSCPPs), namely rhombus tilings ofa 2n × 2n × 2n hexagon of triangular lattice,by means of the three elementary rhombi ob-tained by gluing two elementary triangles alongan edge. Kuperberg extended the counting toinclude ASMs with various symmetries, in rela-tion to plane partitions with various symmetries.His original method relies on a bijection betweenASMs and congurations of the 6 Vertex modelon an n×n grid of square lattice, and variationsthereof.

With the Razumov-Stroganov conjecture,now proved in a purely combinatorial way byCantini and Sportiello (2010), yet another phys-ical statistical model was introduced into thegame: a dense loop model on a semi-innitecylinder of square lattice with xed perimeter2n.

Our chief weapon is integrability, allowing for

exact solutions. In [t07/224], we use methodsborrowed from quantum integrable systems tocompute certain correlations of the loop gas in asemi-innite strip, as illustrated in Fig.A.12. Inparticular, we nd the relevant solutions of thequantum Knizhnik-Zamolodchikov equation sat-ised by the groundstate of the model, via multi-residue integral representations, and the exten-sive use of representations of the Temperley-Liebalgebra.

As a by-product, we get a closed expres-sion for the sum of the un-normalized congura-tion probabilities in the groundstate of the denseloop gas for strip width N , identied in vari-ous limits of the parameters of the model withpartition functions for: (i) the Vertically Sym-metric Alternating sign Matrices (VSASMs) ofsize N + 1 = 2n + 1 for even N and (ii) theCyclically Symmetric Transpose Complemen-tary Plane Partitions (CSTCPP) of size N − 1,represented in Fig.A.13 for odd and even sizes.

The original ASM conjecture formulated byMills, Robbins and Rumsey in 1983 concernedyet another combinatorial object called De-scending Plane Partitions (DPPs), and estab-lished a connection between multiply renedcounting thereof and ASMs. The counting ofDPPs was done by Andrews in the late 70s, butthe above connection with ASMs, whose count-ing is the same, remains mysterious, in partic-ular no natural bijection between the objects isknown to this day. The Mills-Robbins-Rumseyconjecture remained open for 28 years, and ourpaper [t11/048] nally gives its complete proof.We rst use the Kuperberg connection of ASMsto the 6 Vertex model to actually compute thepartition function of the homogeneous 6 Ver-tex model as a simple determinant. Next, weuse the reformulation of DPP in terms of non-intersecting lattice paths, to express the parti-tion function as another determinant. Finallywe connect the two by use of the generatingfunctions for the matrix elements within the de-terminants, also identied as the transfer ma-trix for 1+1-dimensional Lorentzian triangula-tions in innite size. We may summarize theessence of this proof as yet another triumph ofquantum integrability: (i) that of the 6 Ver-tex model, allowing for rephrasing the partitionfunction in determinantal terms (ii) that of non-intersecting lattice paths, also expressible as freefermions (iii) that of Lorentzian gravity in 1+1dimension, via commutation of transfer matrices(Di Francesco, Guitter, Kristjansen, 1999).




1 2 3 4 5 61 2 3 4 5 6

Figure A.12: A typical conguration of the dense loop gas on a semi-innite strip, and the corre-lation function this conguration contributes to, namely the non-crossing pattern of connectionsof the 2N = 6 loop ends of the boundary.

Figure A.13: Typical congurations of the CSTCPP for respectively odd (N = 5) and even (N = 4)sizes. The odd size includes a central triangular hole of size 2× 2× 2.

A.13.2 Combinatorics of alternating signmatrices and of Gessel's conjec-ture (A. Ayyer)

As explained in Section A.13.1, alternating signmatrices are related to fully packed loops (FPLs)and to the Razumov- Stroganov conjecture, nowthe Cantini-Sportiello theorem. In [t08/247](with D. Zeilberger) we attempt to prove theconjecture using a bijectional approach. Wehave been unsuccessful but we believe the tech-niques we present can be used to give an alter-native proof of the conjecture.

Alternating sign matrices are known to beequinumerous with descending plane partitions,a class of plane partitions introduced by GeorgeAndrews in 1979. Mills, Robbins and Rum-sey noticed startling numerical coincidences be-tween rened enumeration of these two struc-tures in 1983. However, there is no known bi-jection between these objects. In [t09/156] a bi-jection is proven between a natural subset of de-scending plane partitions and permutations us-ing the ascent statistic.

Totally symmetric self-complementary planepartitions (TSSCPPs) are yet another class ofplane partitions known to be enumerated by thealternating sign matrix numbers. Once again,Mills, Robbins and Rumsey noticed startling nu-merical coincidences between rened enumera-tion of TSSCPPs and alternating sign matricesin 1986. No bijection is known between any of

these three objects. In [t11/105] (with R. Coriand D. Gouyou-Beauchamps) we nd a natu-ral bijection between subclasses of these usingmonotone triangles. Since alternating sign ma-trices are natural generalizations of permuta-tions, there is a notion of pattern-avoidance forthese too. We show that those alternating signmatrices in bijection are those which, in a veryprecise sense, avoid the pattern 312.

In 2001 Ira Gessel conjectured a formulafor the number of walks in the rst quadrantof Z2, built out of 2n steps in the directions(1, 1), (1, 0), (−1, 0), (−1,−1), starting and end-ing at the origin. In a remarkable tour deforce, Gessel's original conjecture has been -nally proven in 2008 using computer algebratechniques by M. Kauers, C. Koutschan, and D.Zeilberger. To give a simpler proof of Gessel'sconjecture, in [t09/025] we interpret walks in therst quadrant with the abovementioned stepsas a generalization of Dyck words with two setsof letters. Using this language, we give a formalexpression for the number of walks in the stepsabove beginning and ending at the origin. Wegive an explicit formula for a restricted class ofsuch words using a correspondance between suchwords and Dyck paths. Finally we remark on an-other combinatorial problem in which the sameformula appears and argue for the existence of abijection.






A.13.3 Limit shapes in tiling/dimer sys-tems (P. Di Francesco)

Geometrically constrained statistical modelsdefy the general principles in that the con-straints make them very dependent on theirboundary conditions. A large class of such mod-els are dimer models, namely the compact cov-ering of xed bipartite graphs with dimers, i.e.mutually excluding pairs of neighboring vertices.Dimers have received much attention recentlyfrom a new approach to their thermodynamicsusing hydrodynamic equations (Wilson, Propp,Kenyon, Okounkov, Reshetikhin), establishingin particular the existence of frozen regionsof ordered dimers separated from disordered re-gions with nontrivial entropy via arctic curves.The frozen regions are clearly induced by theshape of the boundary, to which the arctic curveis tangent.

In [t09/234], we investigate the case of par-tially free boundaries on dimer models. We usethe formulation of dimer models on the hexago-nal lattice via non-intersecting lattice paths, andstudy their asymptotics via saddle-point tech-niques. In this case, the dimer congurationsare in bijection with rhombus tilings of corre-sponding domains of the triangular lattice (inthe same spirit as for Plane Partitions), and lat-tice paths are easily obtained by following suc-cessions of two types of rhombi throughout theconguration. They can also be interpreted asviews in perspective of 3D piles of unit cubesin domains made of the intersection of severalpositive octants of the 3D space.

A.13.4 Discrete integrable systems,quantum spin chains and clusteralgebras (P. Di Francesco)

This work is a new collaboration with Rinat Ke-dem (University of Illinois, Urbana-Champaign)aimed at better understanding the combina-torics of discrete integrable systems. The lattermay be viewed as dynamical systems in discretetime, with suciently many conserved quanti-ties.

Examples arise from the study of complete-ness of the Bethe Ansatz solution to inte-grable quantum spin chains with the symme-try of some Lie group, where it is shown thatthe state counting amounts to representation-theoretic statements on fusion coecients, alsoexpressed via non-linear recursion relationsbetween characters of some special modules(Kirillov-Reshetikhin, 1988), called Q or T-systems (the latter include an extra spectral pa-rameter, related to the quantum parameter of

the spin chain, and are connected to the so-calledY-systems arising from Thermodynamic BetheAnsatz solutions to quantum spin chains). In[t07/210] we give a proof of the so-called combi-natorial Kirillov-Reshetikhin conjecture by useof generating functions for generalized charac-ters.

More generally, we have investigated thefull spectrum of solutions of Q and T systems,viewed as discrete dynamical systems, in termsof their initial data. In [t08/255], we rst estab-lished a connection between Q and T-systemsand a mathematical structure known as Clus-ter Algebras, introduced in 2000 by Fomin andZelevinsky. A cluster algebra describes the evo-lution of a data vector attached to each vertex ofan innite Cayley tree, subject to specic mu-tations along the edges of the tree, governed bya skew-symmetric exchange matrix often rep-resented as a quiver, also mutated across edges.The dening axioms for mutations are such thatthey guarantee the Laurent property, namelythat any mutated data can be expressed as aLaurent polynomial of the data at any other ver-tex of the tree. Fomin and Zelevinsky put for-ward the conjecture (still open to this day) thatthe coecients of these Laurent polynomials arenon-negative integers. It is a challenge to nd acombinatorial/statistical physics interpretationfor these.

The structure of cluster algebra appears inmany dierent mathematical and physical con-texts, such as: Somos sequences (non-linearrecursion relations), quiver representation the-ory (category theory), surgery of Teichmüllerspace and triangulations (geometry), total pos-itivity of Grassmannians (linear algebra), net-work theory and non-intersecting lattice paths,wall-crossing for Donaldson-Thomas invariants(algebraic geometry and string theory).

Our systems are very special in the clusteralgebra world: they turn out to be integrable,i.e. to have suciently many conserved quanti-ties to be amenable to exact solutions in termsof initial data. In [t08/256], we show that thesolutions of the Q-system for the Ar Lie al-gebra may be expressed in terms of partitionfunctions for discrete paths or families of dis-crete non-intersecting paths on suitable targetgraphs, with step weights that are positive Lau-rent monomials of the initial data, thereby prov-ing the Fomin-Zelevinsky positivity conjecturefor these particular cluster algebra mutations.We found a remarkable formulation for the clus-ter mutations in terms of local rearrangements of(possibly branching) continued fractions, whose






αΓ

M2n+2 −2

Figure A.14: A typical congurations of dominos and defects covering a domain whose shape isdetermined by the initial data of the Q-system. We have also represented the underlying non-intersecting paths and the target graph on which they are travelled, also determined by the initialdata.

shape is determined by initial data. We alsoprovided an alternative combinatorial interpre-tation of the solutions as partition functions fordomino tilings of deformed Aztec diamonds ofthe square lattice using standard 2×1 and 1×2dominos, as well as defects (see Fig.A.14).

More exact results were obtained in[t09/233], [t09/235], [t10/231] on the T-systemas well, by reformulating the former in termsof electrical networks, namely weighted non-intersected lattice paths on graphs obtained bygluing elementary electrical chips, in the samespirit as the canonical decomposition of totallypositive GLn matrices into products of elemen-tary upper and lower triangular matrices.

The simplicity of our solution allowed foran immediate extension to the case of non-commutative variables, this time in the formof discrete path partition functions with non-commutative step weights multiplied in the or-der in which the steps are taken. In particularwe proved a conjecture by Kontsevich [t09/236]related to wall-crossing for non-commutativeDonaldson-Thomas invariants. More generally,we designed a framework for a non-commutativeversion of the Q-system [t10/119], [t10/232],based on the theory of quasi-determinants ofGelfand-Retakh. It involves a non-commutativegeneralization of multiply branching continuedfractions and their local rearrangements. Thecorresponding non-commutative Q-systems in-clude as a special case the so-called quantum Q-systems, associated to quantum cluster algebras.The latter were dened in 2005 by Berensteinand Zelevinsky as a natural quantization of thenotion of cluster algebra, and bears connectionsto the questions of positivity of Lusztig's canon-ical bases of quantum enveloping algebras. Fi-

nally, in [t11/047] we introduced a quantum ver-sion of the T-sytsem for sl(2) based on the asso-ciated quantum cluster algebra, and constructedits solutions for arbitrary initial data in terms ofnon-commutative networks. In particular, thissolution allowed us to prove the quantum versionof the Fomin-Zelevinsky positivity conjecture forthe associated quantum cluster algebra.

A.13.5 Labelled positive paths andmatchings (B. Duplantier)

In the joint work [t09/036] with O. Bernardi(Orsay) and P. Nadeau (Vienna), we study thepartition function of a three-dimensional freely-jointed chain (FJC) of n steps, anchored at aplane in a half-space (a model of interest to bi-ological physicists for describing the microma-nipulation of DNA chains). This problem isfound to require a combinatorial treatment. Ofparticular interest is the n-dimensional polytopeΠn in Rn consisting of all points (x1, . . . , xn) ∈[−1, 1]n such that

∑ji=1 xi ≥ 0 for all j = 1 . . . n,

whose volume gives the partition function of theFJC (at zero tensile force).

It is shown in [t09/036] that a collection of n-dimensional subpolytopes partitioning the poly-tope Πn is in bijection with a set of so-calledwell-labelled positive paths. A well-labelled pos-itive path of size n is made of a sequencep1, p2, . . . , pn−1 of discrete steps −1, 0,+1such that

∑ji=1 pi ≥ 0 for all j = 1 . . . n− 1,

together with a permutation σ1, σ2, . . . , σn of1, . . . , n such that pi = −1 implies σi < σi+1,while pi = 1 implies σi > σi+1. The generat-ing functions of those paths and their Motzkincounterparts are evaluated by coupled recur-sions. We also establish a bijection between well-labelled positive paths of size n, labelled binary











trees, and matchings (i.e. xed-point free in-volutions) on 1, . . . , 2n. This proves in par-ticular that the number of well-labelled positivepaths is (2n− 1)!! ≡ (2n− 1) · (2n− 3) · · · 3 · 1.Given that the volume of each subpolytope is1/n!, our results prove combinatorially that thevolume of Πn, i.e., the partition function of theoriginal FJC, is (2n−1)!!

n! . By specializing our bi-jection, we prove a series of other combinatorialresults, such as the number of permutations ofsize n such that each prex has no more ascentsthan descents being [(n− 1)!!]2 if n is even andn!! (n − 2)!! otherwise. The complete study ofthe FJC partition function with a non-vanishingtensile force will be the subject of a forthcomingpublication.

A.14 Sigma models on super-manifold targets: structuresand applications

Two dimensional non-linear sigma models withsuper-manifold target spaces have emerged in awide variety of systems, and their study has be-come increasingly relevant for some of the mostchallenging problems of modern physics.

In condensed matter, super-manifold targetspaces arise mostly in the supersymmetric ap-proach to non-interacting disordered systems.The transition between plateaux in the integer(2+1 dimensional) quantum Hall eect is for in-stance believed to be related to the sigma model(1 + 1 dimensional) U(1,1|2)/U(1|1) × U(1|1) atθ = π, a conformal eld theory which has notyet been understood, despite decades of work.Other super sigma models arise in the descrip-tion of similar phase transitions belonging to dif-ferent universality classes. Of particular recentinterest is the transition between plateaux in the`spin quantum Hall eect' (Class C) observed indirty d + id superconductors (see below). Su-permanifold targets also arise in the study ofgeometrical problems, such as percolation, poly-mers etc.

In string theory, super-group and super-cosettargets play an important role in the Green-Schwarz or pure spinor type formulation, wheresupersymmetries act geometrically as isometriesof an underlying space-time (target space) su-permanifold. Important examples arise in thecontext of the AdS/CFT dualities between su-persymmetric gauge theories and closed strings.For instance, it has been known for a few yearsthat string theory on AdS3 × S3 could be quan-tized if it were possible to construct conformalquantum eld theories with a PSL(2|2) targetspace.

In addition to such concrete applications,there exists a number of fundamental reasonsto be interested in particular in conformal σ-models with target space (internal) supersym-metry. Being non-unitary, the relevant con-formal eld theory models exhibit rather un-usual features such as the occurrence of re-ducible but indecomposable representations andthe existence of logarithmic singularities (on theworld-sheet). The resulting issues of non semi-simplicity have profound mathematical connec-tions. On the other hand, the special prop-erties of Lie supergroups allow for construc-tions which are not possible for ordinary groups.For instance, there exist several families of su-pergroup σ-models which admit a new kind ofmarginal deformations that are not of current-current type. The solution of these models isone of the most tantalizing modern problems inthe eld.

A.14.1 Conformal sigma models on su-pergroups: lines of CFT (C.Candu, J.L. Jacobsen, H. Saleur)

The simplest conformal σ-model is probablythe supersphere sigma model, that is the cosetOsp(2n+2|2n)/Osp(2n+1|2n). The case n = 0is nothing but the ordinary O(2) sigma model(the free boson), which pretty much guaranteesvanishing of the beta function to all orders, andthe existence of a line of conformal eld theorieswith properties depending on the sigma modelcoupling g2

σ. Like for all the other super sigmamodels, non-unitarity precludes the use of stan-dard techniques to calculate the spectrum andthe correlation functions. To make progress,Candu and Saleur in [t07/166] and [t07/167]rst obtained a lattice regularization of the CFTbased on an orthosymplectic superspin chain.They then performed a decomposition of theHilbert space in terms of representations of theosp algebra and its centralizer, which in this caseturns out to be (a quotient of) the Brauer alge-bra. Because the algebras involved are not semi-simple, this decomposition is complicated, in-volves various types of indecomposable modules,and relies in part on some very recent results inthe theory of cellular and quasi-hereditary al-gebras. On the other hand, there is a growingexpectation - justied in part by results fromRead and Saleur in the previous period [t06/136,t06/154] - that the resulting `bimodule' struc-ture is essentially independent of the size of thelattice, and identical with the one of the contin-uum limit. Using this idea, Candu and Saleurwere able to conjecture the full structure of the




boundary CFT (with Neumann boundary con-ditions), including the structure of the Virasoromodules, and the exact dependence of the con-formal weights on the coupling constant. Theywere also able to conjecture a duality betweenthe super sphere sigma model and the orthosym-plectic Gross Neveu model. Part of these resultswere later proved in works by Schomerus andcollaborators.

Later, Candu, Saleur and collaborators inHamburg performed in [t09/193] a similar analy-sis for the superprojective sigma model CPn−1|n

which, this time, gives rise to a line of CFTsat central charge c = −2, the n = 0 casebeing nothing but the symplectic fermion the-ory. On top of the algebraic analysis, theyalso performed perturbative expansions at weakcoupling and minisuperspace analysis, and con-cluded to the absence of duality with the GrossNeveu model, for yet unknown reasons. Theyalso investigated in details the role played by thetopological angle and the boundary, with poten-tial applications to the study of edge states intopological insulators (see below).

Meanwhile, the conformal sigma models canbe interpreted in terms of geometrical models ofstatistical mechanics. The most striking conse-quence is that, if one takes dense polymers (cor-responding to packed self avoiding walks, forcedto occupy a non vanishing fraction of the avail-able space) and allows for 6 legs crossings, anew universality class is obtained, with expo-nents varying continuously [t09/194].

A.14.2 CPn+m−1|n models at θ = π:strong coupling physics (R. Bon-desan, J. Dubail, J.L. Jacobsen, H. Sa-leur)

While models such as the supersphere sigmamodel can be at least partly understood usingperturbation theory, there are many other cases- and the model expected to describe the criticalproperties at the transition between plateaux inthe integer quantum Hall eect is of this type- where the interesting physics occurs only atstrong coupling. The simplest example in thiscontext is provided by the (more general) σ-models on superprojective spaces CPn+m−1|n =U(n+m|n)/[U(1)×U(n+m−1|n)] at θ = π, inparticular the models CPn|n which are expectedto ow to CFTs with vanishing central charges.In previous work, Read and Saleur had man-aged to nd the spectrum of exponents for thesetheories in the bulk [t01/197]. In the recentwork [t11/056], Bondesan, Jacobsen and Saleurmanaged to solve the strong coupling CFT in

the presence of boundaries. This is particularlyinteresting as it gives a way of understandingthe spectrum for dierent values of the topolog-ical angle θ = π modulo 2π. Indeed, while bulksigma models are expected to only be sensitive tothe value of θ up to multiples of 2π, in the pres-ence of boundaries, the exact value of θ matters.In fact, this value is what makes the dierencebetween the dierent plateaux transitions in theHall eect. It corresponds, physically, to the ex-istence of additional edge states on the bound-ary of the sample. In [t11/056], the surprisingresult was obtained that for CPn|n and θ > π(θ = 3π, 5π etc) the exponents are in fact ir-rational. Their values result from an extremelytechnical analysis based on loop models, whichwill be described partly below. The interestingpoint is that these exponents have an immediatetranslation in terms of transport properties forthe class C disordered systems. In a paper withI. Gruzberg and H. Obuse, Bondesan Jacobsenand Saleur have analyzed transport in the cor-responding Chalker Codington disordered net-work model, and found remarkable agreementwith their analytical predictions.

A.14.3 RG ows in super Gross Neveumodels (B. Pozsgay, H. Saleur)

The challenge of sigma models with super-targets goes beyond the study of their confor-mal limits. Like their ordinary cousins, modelssuch as the orthosymplectic (orthogonal) GrossNeveu model for instance appear formally in-tegrable, and attempts have been made overthe years to write their S matrices and analyzetheir physical properties. Considerable dicul-ties are however encountered, once again due tonon unitarity - typically, in the case of super-groups, probability is only conserved with re-spect to a non positive metric. Put it otherwise,events with negative probabilities have to for-mally be included. In [t09/195] Poszgay andSaleur investigated the particular case of theOSp(2|2) Gross Neveu and supersphere sigmamodels, and attempted to connect the S matriceswith a thermodynamic Bethe ansatz. We uncov-ered fascinating duality properties, relating forinstance the ground state energy of these theo-ries with the one of ordinary theories - namelythe SO(4) sigma and Gross Neveu models re-spectively - generalizing earlier observations forthe OSp(4|2) case. They also studied the pos-sibility of nding an integrable ow into theGross Neveu model, which could then originateat the non trivial Nishimori critical point of therandom bond (strongly) disordered Ising model.







Unfortunately, they concluded that such owsdid not have a non trivial origin, showing thatthe Nishimori point is inaccessible by integrabletechniques.

A.14.4 Sigma models and loop models(J. Dubail, J.L. Jacobsen, H. Saleur)

It is increasingly clear that the properties ofthe sigma models of interest in condensed mat-ter physics are profoundly related with those ofloop models. This correspondence comes for-mally from the diagrammatic representation ofcentralizer algebras going back at least to Brauer(1937). Physically, it nds it origin in the net-work models à la Chalker Coddington, and ulti-mately, in the properties of trajectories of ran-dom electrons in two dimensions. In a seriesof articles dating back to [t06/155], Jacobsenand Saleur have focussed on the role of bound-ary conditions in loop models, uncovering verycomplex structures with many potential appli-cations. In [t09/071] and [t09/073], they havesolved the more general problem of loop modelson annuli subject to dierent boundary condi-tions on the left and right hand sides. This isprofoundly related to the study of centralizers ofspin chains with higher spin representations atthe extremities (and thus, to the physics of edgestates, see above). The technology to solve thisproblem relies largely on representation theoryof the two boundary Temperley Lieb algebra,which was pioneered by Saleur [t94/188], andhas drawn ever more attention from the mathe-matics community.

A.14.5 Logarithmic CFT (J. Dubail, A.Gainutdinov, J.L. Jacobsen, H. Sa-leur, R. Vasseur)

The CFTs associated with the sigma models areall logarithmic - which in essence means that therepresentations of their chiral algebra (Virasoroetc) come in dierent varieties, some of them be-ing only indecomposable instead of irreducible.This has profound consequences, and makes theabstract study of these CFTs proverbially di-cult. The parallel drawn in [t06/136] by Readand Saleur with non semi simple Lie algebrasand their centralizers has grown to become oneof the main tools in the eld. Recently, VasseurJacobsen and Saleur [t10/021] were able to pushthis relationship to measure indecomposabilityparameters (parametrizing Jordan cells of theL0 generator) in the case of polymers and per-colation. Our result profoundly aected the sta-tus quo in the literature, and opened the wayto a better understanding of LCFTs at vanish-

ing central charge in particular. The analysiswas generalized further in [t11/057] to severalfamilies of LCFTs. As a result, the relation-ship between lattice and continuum limit alge-bras appears ever deeper. Moreover, all the toolsare now ready to tackle the case of bulk LCFTs,which is technically considerably more dicult,as the usual relationship between boundary andbulk CFTs does not appear to generalize in anysimple way to the logarithmic case. Saleur andcoworkers have many preliminary results in thisdirection, which will be their main focus in theyear to come.

The mathematical structures unraveled bythe analysis of lattice models are of interest intheir own right. In particular, the emergence ofthe full or Lusztig quantum group at root ofunity to describe (1, p) logarithmic theories with

central charge c = 1− 6 (p−1)2

p suggests to studyfusion in LCFT exactly using the same principlesas in the lattice, Temperley Lieb based analysis,pioneered by Read and Saleur in [t06/136]. A.Gainutdinov and coworkers explored various as-pects of this idea, and built in particular the fullfusion algebra of the (1, p) models in [t11/086].

A.15 Quantum eld theory oncurved spaces

A.15.1 Field quantization in curvedspace (R. Schaeer)

In curved spaces it naturally occurs that a givencoordinate set covers only part of the wholespace. In this case, the remainder is classicallynot accessible. The question then is to deter-mine to which extend this next world can weightup the events in our accessible space. Quantumeects connect the two. Depending on the physi-cal description of the system one considers, how-ever, this next world may be from inexistent upto determinant for the occurrence of events herebelow; violently antagonist views of our worldindeed? vain antagonism, just a gage choice?General Relativity indeed tells us that the de-scription of a physical state is to be independentof the coordinate system choice.

The resolution of this dilemma requires togo beyond the Feynman rule, that in Minkowskispace selects the unique vacuum where elemen-tary excitations are solely positive energy states.Several examples show such a move is neces-sary [t07/121] in de Sitter space to preserve thede Sitter invariance under a change of coordi-nates; more generally to insure a given phys-ical state indeed yields equivalent expectationvalues of observables whatever the coordinate








representation, as required by Einstein's princi-ple. The step to insure the latter is to pin down[t08/277, t09/297] the most general quantizationallowed in curved space. Lifting the Feynmanrule then unravels a vast area of new possibil-ities with potentially unexpected consequences,still under exploration.

A.15.2 From startriangle integrals onLobatchevski space to Källen-Lehmann representations of per-turbative two-point functions inthe de Sitter universe (J. Bros, M.Gaudin, V. Pasquier)

In collaboration with H. Epstein and U.Moschella [t09/269], we produce a seeminglyundiscovered formula for a certain integralh(κ, ν, λ) of the product of three generalizedLegendre functions of the rst kind with re-spective parameters κ, ν, λ. Such Legendre-typefunctions have an interesting interpretation asbeing the two-point functions of free Quan-tum Field Theories (QFT) with three dierentmasses κ, ν, λ on the (d−dimensional) de Sit-ter spacetime, while the integration manifold forthis triplet is the Lobatchevskian submanifold ofthe complexied de Sitter hyperboloid.Two types of comments are relevant:

1) from the viewpoint of mathematics: ablending of geometrical ideas and analytic meth-ods is used for computing the quantity h(κ, ν, λ)on the basis of a generalized star-triangle iden-tity. The latter involves the integration on tri-angles on the asymptotic cone of the de Sitterhyperboloid, which is implemented (thanks toa beautiful geometrical identication) in an oldwork by one of us (M.G) on Clebsch-Gordan co-ecients.

2) from the viewpoint of QFT on the de Sit-ter universe: h(κ, ν, λ) turns out to provide theKällen-Lehmann weight ρν,λ(κ) of the bubble di-agram of two massive elds with given masses νand λ, expressed as a linear superposition of free-eld two-point functions with mass κ. Thereby,this computation allows one to generalize thestudy of particle decay in de Sitter space-timeas given by rst-order perturbation theory in aLagrangian interacting quantum eld theory: ina previous work by one of us (J.B.) and H. Ep-stein and U. Moschella (see [t08/272] and a shortversion of it reported in the previous rapportd'activité de l'IPhT: 2005-2007) the case of adisintegration in two equal mass particles (i.e.ν = λ) has been treated completely, thanks tothe computation of h(κ, ν, ν) which was muchsimpler. In that special case, a complete analy-

sis of the lifetime of a de Sitter particle is givenin [t08/272], including the extension to cases ofmasses κ in the complementary series of the deSitter group and the proof that the lifetime of ade Sitter particle is independent of its velocitywhen it is of the order of the de Sitter radius.

Then, thanks to the general computation ofh(κ, ν, λ) given in [t09/269], all the aspects ofthe analysis of [t08/272] can be transported tothe case of disintegration in two particles withunequal masses.

A.16 Generalized interval ex-change maps (P. Moussa)

Following previous papers [t03/033, t04/046], incollaboration with S. Marmi and J.-C. Yoccoz,we have obtained new results in the study of in-terval exchange maps. Such maps are interestingexamples of mathematical dynamical systems,since they generalise rotations on a 2D torusto similar transformations on Riemann surfacesof higher genus. They are also associated withrational pseudo-integrable billard maps. Thestudy of interval exchange maps is itself a chap-ter of ergodic theory of dynamical systems.

When the exchange is realised through atranslation, the exchange maps is said to bestandard. In [t08/112] the authors have con-sidered ane interval exchange maps, includinga further linear rescaling. They show that al-most all such maps have wandering intervals,which implies that they are not conjugated, butonly topologically semiconjugated to a standardexchange map. In [t10/234] the analysis is ex-tended to generalized exchange maps, where thetransformations are deformations of translationswith some regularity properties. Among suchtransformations, we characterize those which areconjugated to standard maps: within the man-ifold of all possible deformations, they form asubmanifold of specied codimension.

A.17 Stochastic dynamical sys-tems (K. Mallick)

Randomness in the external conditions entailsthe parameters of a system to uctuate and cantherefore be modeled as multiplicative noise inthe dynamical equations. Our aim in the follow-ing works was to investigate how the interplayof noise and nonlinearity in a system far fromequilibrium can drastically alter the propertiesof the dynamics both qualitatively and quanti-tatively and induce some unusual phenomena.











A.17.1 Dynamical systems subject togeneral noise

A noise acting on a dynamical system can dras-tically modify an instability process. In partic-ular, a multiplicative noise can lead to a newtype of intermittency, called OnO intermit-tency, in which quiet and laminar (o) phasesrandomly follow bursting (on) phases. This in-termittency has been identied in various exper-iments. Most theoretical works consider white orOrnstein-Uhlenbeck noises. However, in realis-tic situations, the noise is far from being white.In [t07/170] we discuss the dependence of theintermittency on the Power Spectrum Density(PSD) of the noise. We derive analytical resultsfor some particular types of noises and performa cumulant expansion for an arbitrary PSD. Weshow that the intermittent regime is controlledby the ratio between the departure from thethreshold and the value of the PSD at zero fre-quency. Our results are in agreement with nu-merical simulations (joint work with F. Petrélis,ENS Paris and S. Aumaître, CEA)

In [t07/212, t09/049] we use an eectiveMarkovian description to study the long-timebehavior of a nonlinear second-order Langevinequation subject to a Gaussian noise with ar-bitrary spectrum (provided the spectrum decaysalgebraically at high frequencies). We analyti-cally compute the probability distribution func-tion in phase space in the long time limit. Thisleads to scaling formulae for the growth of theamplitude, of the momentum, and of the energytransfer. In particular, we show that the scalingexponents depend on both the stiness of theconning potential at innity, and the smooth-ness of the random excitation: the smoother thenoise (which corresponds to a faster decay of thepower spectrum at high frequencies) the less ef-cient the energy transfer from the bath to theoscillator. At large times the system reaches anonequilibrium steady state in which physicalobservables do not grow anymore; the crossoverfrom power-law growth to this steady state oc-curs when the rate of energy dissipation by fric-tion matches that of energy absorption from therandom environment.

A.17.2 Diusion and multiplication in arandom medium

In [t10/191], we investigate the evolution ofa population of non-interacting particles whichundergo diusion and multiplication. Diusionis assumed to be homogeneous, while multipli-cation proceeds with space dependent rates, re-ecting the nonhomogeneous distribution of nu-

trients. The latter distribution denes a land-scape, which is assumed to be a stationary andquenched random variable with zero average (sothat the population size would remain constantif the distribution were homogeneous). The uc-tuations drastically aect the behavior of thepopulation size, and dierent statistical proper-ties of this landscape lead to a number of laws forthe growth of the population. We show that inmost cases, the total population increases fasterthan exponential. This behavior is due to twofeatures of the noise, namely its multiplicativenature, and its unboundedness. Another strik-ing feature is the huge dierence between typicaland average behaviors. In order to determine theaverage growth law, one has to consider all pos-sible realizations of the random landscape, andthe average is dominated by rare congurationsin which extremal statistics play an importantrole. We have performed asymptotically exactcalculations in the situation where the landscapeis described by a Brownian noise. There, thedetermination of the average population growthreduces to calculating a rst passage exponentialfunctional of the Brownian motion, which can bedone exactly. More general cases are analyzedthrough heuristical predictions. (joint work withP. Krapivsky, Boston University).

A.17.3 Localization in the non-linearSchrödinger equation

In [t08/133] we consider the problem of the one-dimensional Anderson localization for the non-linear Schrödinger equation (NLS). The basicquestion is to investigate whether Anderson lo-calization can survive the eects of nonlineari-ties. This problem is relevant for experiments innonlinear optics (e.g. disordered photonic lat-tices). We show that the asymptotic growth ofthe moments of a stationary wave function forNLS (and of its derivative), can be determinedknowing the corresponding growth rates for thelinear Schrödinger equation. Using a mappingto a Langevin equation, we compute the latterrates (and in particular the behavior of high or-der cumulants). Finally, a resummation proce-dure is used to deduce the results for the nonlin-ear Schrödinger equation, in particular and thelocalization length of the stationary states (jointwork with S. Fishman and A. Iomin, Technion,Israel).

A.18 (Magneto-)hydrodynamicalinstabilities (Ch. Normand)

Axisymmetric ows, ubiquitous in Nature, arethe source of various instabilities in uid dynam-







ics. Helical ows in a conducting uid are atthe origin of growing magnetic elds (dynamoeect); this eect is studied both for steadyand for time dependent ows. Centrifugally sta-ble circular Couette ows can become unstablewhen they take place in a stably stratied uid,the onset conditions are studied for an inviscidow.

A.18.1 Energetic stability of cylindricaldynamos

In [t08/032] a cylindrical dynamo problem isstudied through a Galerkin expansion of themagnetic eld components. Thresholds for theenergy instability of the system are estimated,in the form of lower bounds for the critical mag-netic Reynolds numbers REm for dierent az-imuthal modes m. The value of REm for the mostunstable modes (axisymmetric and antisymmet-ric) are found to be close to each other, so thatone may expect mode coupling through the feed-back on the velocity eld. This mechanism couldexplain the eventual growth of the axisymmetricmode, which is otherwise excluded by the usualmodal stability analysis.

A.18.2 Helical dynamos driven by sto-chastic ows

Investigating the role of turbulence on dynamoaction implies to solve the full MHD equations,which can be done numerically only in very spe-cic situations. A simplied problem is to de-termine how the onset of dynamo driven bysteady ows is modied by the addition of time-dependent uctuations, with a temporal behav-ior modelled by a periodic or a stochastic func-tion.

Refs. [t10/079], [t11/052] study the genera-tion of magnetic eld by a helical ow made of amean steady ow plus a random uctuating ow.The steady ow and the uctuations are bothsolid body screw motions with constant pitches,respectively Γ and Γ, and the time dependenceof the uctuation is a Gaussian white noise. Thethreshold shift induced by uctuations of smallamplitude is calculated analytically for dierentvalues of µ = m + kΓ and µ = m + kΓ, m andk being the axial and azimuthal wavenumbersof the growing magnetic eld. A steady ow isoptimized for dynamo action when the dynamothreshold Rc is minimum. For helical ows itoccurs when the pitch of the magnetic helicallines, |m/k|, and the pitch of the ow satisfy thecondition of spatial resonance µ ≈ 0. We ndthat, for small enough values of µ, the thresholdRc can be lowered by the addition of the small

random uctuating ow, provided µ belongs toan appropriate interval near 0. The conclusionis that optimized uctuations are benecial todynamo action driven by helical ows.

Ref. [t11/052] also considers a purely uctu-ating ow, with temporal uctuations modelledby a colored noise, and investigate the inuenceof the correlation time on the dynamo onset.

A.18.3 Strato-rotational instability

The strato-rotational instability (SRI) occurringin stably stratied rotating ows is a possiblesource of turbulence in Keplerian accretion disksand in oceans. In the laboratory, SRI was de-tected in experiments on a circular Couette ow(CCF) between two concentric cylinders of radiiR1 and R2 rotating at angular velocities Ω1

and Ω2, respectively. In the small gap limitR1/R2 = η → 1, the modied Rayleigh crite-rion for SRI in inviscid uids, Ω1/Ω2 = µ < 1,is unable to account for the fact that unstablemodes were experimentally observed only whenµ < η. In numerical simulations of viscous CCF,SRI was found when µ < µ∗, with µ∗ being ei-ther larger or smaller than η.

Ref. [t09/185] analyses the inuence of nitegap eects on the stability criterion. The invis-cid dispersion relation is derived analytically fornon axisymmetric perturbations and the exactvalue of the growth rate is computed for threerepresentative values of η. For a given value of µ,unstable modes are found on a bounded intervalof axial wavenumbers. As µ increases, the inter-val becomes narrower and shifts towards higherwavenumbers values. Wavenumbers observed inexperiments and computations fall inside the in-terval predicted by the theory provided µ < µs,with values µs ≥ η when η → 1 and µs < ηwhen η → 0, in agreement with the stability lim-its found in the available data. It is concludedthat viscous damping of the modes with largewavenumbers is responsible for the disappear-ance of SRI when µ > µs.

A.19 Dynamics of quantum deco-herence and random matrixmodels (F. David)

The study of decoherence and dissipation inopen quantum system is an established sub-ject, of crucial importance in condensed matterphysics, atomic and quantum physics, quantuminformation, and especially for a proper under-standing of the quantum formalism and of thequantum measurement processes. Random ma-trix methods have been used since a long time,as a way to model the complicated dynamics







and couplings between a simple quantum sys-tem and the external environment. Most estab-lished results are valid in the so-called Marko-vian regime, where the dynamics of the environ-ment is fast, so that quantum memory eectscan be neglected.

Motivated by the search of a better under-standing of the general regime, we have proposedand solved a simple but very general quantummodel of an SU(2) spin interacting with a largeexternal system with N states [t10/134]. Thecoupling is described by a random hamiltonianin a new general gaussian SU(2)×U(N) randommatrix ensemble. The model is solved in thelarge N limit, for any value of the spin j and forany choice of the coupling matrix element distri-butions in the dierent possible angular momen-tum channels l (and provided that the internaldynamics of the spin is slow). Besides its math-ematical interest as a non-trivial random matrixmodel, this model allows to study and illustratein a simple framework various important quan-tum phenomena: the decoherence dynamics, theconditions of emergence of classical degrees offreedom and of the classical phase space for thespin, the general properties of quantum diu-sion in phase space. The large time evolutionfor the spin is shown to be non-Markovian ingeneral, the Markov property emerging in somevery specic cases, both for the dynamics of theexternal system and the coupling, but also forthe initial conditions.

A.20 Quantum formalism (F.David)

The role of causal reversibility, together withcausality and locality, is stressed in the justi-cation of the quantum formalism in [t11/035].Firstly, in the algebraic quantum formalism,starting from the general notion of states andobservables, it is shown that reversibility impliesthat the observables of a quantum theory forma real C*-algebra. Not so well known GNS-liketheorems from the '60-'70 imply that it can berepresented as an algebra of operators on a realHilbert space. The restriction to standard com-plex C*-algebras and complex Hilbert spaces isrecalled to come from the constraints of localityand separability. Secondly, in the quantum logicformalism, it is discussed which axioms (exis-tence of an orthocomplementation and the cov-ering property) derive from reversibility. Hereagain, assuming locality ensures that the latticeof propositions can be represented as projectorson a complex Hilbert space, and leads to thestandard representation of the quantum formal-

ism.

A.21 Scattering theory with non-local potentials and complexangular momentum theory(J. Bros)

In [t10/142], we have established the meromor-phy properties of the partial scattering ampli-tude T (λ, k) associated with physically relevantclasses of nonlocal potentials, in domains of thespace C2 of the complex angular momentum λand complex momentum k (the square root ofthe energy). In these domains, the general ex-pression of T as a quotient Θ(λ, k)/σ(λ, k) of twoholomorphic functions is obtained by using theFredholmSmithies theory for complex k, at rstfor λ = ` integer, and in a second step for λ com-plex (with <eλ > −1/2). This allows to denethe polar manifold of T by solving σ(λ, k) = 0.

We then justify the Watson resummation ofthe partial wave amplitudes in an angular sectorof the λplane, in terms of the various connectedcomponents of this polar manifold. While inte-grating the standard notion of interpolation ofresonances in the upper halfplane of λ (due toRegge), this unied representation of the singu-larities of T also provides an attractive possibledescription of the echoes (or antiresonances)in the lower halfplane of λ. Such a possibility,which is forbidden in the case of local poten-tials, represents an enriching alternative to thestandard BreitWigner hardsphere picture ofthese echoes. (collab. with E. De Micheli andG.A. Viano).

A.22 Nonhermitian quantumchaos (S. Nonnenmacher, E.Schenck)

Several types of quantum systems lead to con-sider eective nonselfadjoint Hamiltonians ofthe form H = H0 − iεH1, with H0, H1 her-mitian, and ~ ≤ ε 1. The rst example isthe scattering of a particle by a localized po-tential (scatterer). The original Hamiltonian,H0, admits (complex valued) resonances belowthe continuous spectrum; the latter can be ob-tained as eigenvalues of an operator of the aboveform, obtained by deforming H0. Our aim is tounderstand the semiclassical distribution of theeigenvalues of H, using the underlying classicaldynamics. We focussed on scattering systems forwhich the set of (classical) trapped trajectories isfractal, and hosts a chaotic dynamics. For suchsystems, no separation of variables, or normalform, are possible, so the resonance spectrum is





not explicit.

A.22.1 Resonances for chaotic scatteringsystems

In [t07/106], [t09/052] we give a sucient con-dition for the presence of a gap in the resonancespectrum (that is, a resonance free strip belowthe real axis). This condition is expressed by thenegativity a certain topological pressure associ-ated with the classical ow on the trapped set.In two dimensions, this criterium amounts to anupper bound on the Hausdor dimension of thetrapped set. A resonance gap implies strong dis-persive properties for the associated quantum orwave system. (collab. with M. Zworski)

We developed in [t10/055] a new method toanalyze these resonances. The idea is to extractthem from an auxiliary quantum monodromy op-erator, which quantizes the Poincaré map forthe ow. This monodromy operator has simi-lar properties with the open quantum maps usedas a toy model for chaotic scattering systems. In[t11/143] we used this method to show that theresonances in the case of N ≥ 3 convex hard ob-stacles satisfy fractal Weyl upper bounds in thehigh energy limit. (collab. with J. Sjöstrand andM. Zworski)

We are also interested in the shape of theassociated metastable states for such systems.We have shown in [t07/106] that their phasespace distribution can be described by a certainfamily of probability measures, invariant w.r.tothe classical ow up to a global decay. Yet,it remains unclear whether quantum mechanicswill select certain of these measures, as is thecase for closed chaotic systems. This questioncould be partially answered only for a very spe-cic open quantum map in [t08/111]: we showedall the metastable modes of near-minimal decayrate semiclassically have the same phase spacedistribution, but this uniqueness breaks downin the bulk of the spectrum. (collab. withJ. Keating, M. Novaes and M. Sieber).

The review article [t11/144] on spectral as-pects of open chaotic systems summarizes therecent advances described above (and some oth-ers).

A.22.2 Damped quantum systems

The second class of systems consists in dampedwaves propagating on a compact domain (ormanifold): H0 is the free motion, while H1 ≥ 0represents the damping. The spectrum of Hlies in a strip below the real axis. One is inter-ested in the distribution of the imaginary partsof the eigenvalues (quantum decay rates). We

have concentrated on situations where the clas-sical dynamics is chaotic (e.g. a manifold of neg-ative curvature), and the damping function isnonhomogeneous. The distribution of the de-cay rates is then peaked near a typical value,given by the phase space average of the damp-ing. In [t08/055] we estimated the width of thisdistribution for a toy model of damped quantummaps, and established a condition for a spectralgap in terms of a certain topological pressure ofthe classical ow. In [t09/131] the same condi-tion is proved by Schenck in the case of dampedwaves on a manifold of negative curvature, andfrom there one shows that the energy of thewaves decays exponentially. In the frameworkof damped quantum maps, upper bounds forthe density of quantum decay rates away fromthe typical value are established in [t09/013]:these bounds have the form of fractal Weyl laws(namely, fractional powers of ~−1), and the pow-ers correspond to large deviation functions forthe classical chaotic dynamics.

A.23 Quantization and resumma-tion methods in quantummechanics (J. Zinn-Justin)

A.23.1 Multi-instantons and exact quan-tization

The articles [t07/225], [t09/307], [t09/308],[t10/035], [t10/036] are all dierent applicationsof ideas developed by the author in the eight-ies and inferred from multi-instanton consid-erations in the quantum mechanics of poten-tials with degenerate classical minima. Therea generalization of the exact form of the BohrSommerfeld quantization equation was conjec-tured, which was later partially proved. Morerecently, this generalized quantization conditionwas reformulated in the context of the so calledexact WKB expansion, allowing the calculationof many terms of the semiclassical expansion andsystematic numerical checks of the conjecture.In the recent publications a number of applica-tions to other potentials like x2+gxN for a num-ber of values of N , including non-Hermitian PTsymmetric potentials, are studied (collab. withU.D. Jentschura, M. Lubasch, A. Surzhykov).

A.23.2 Orderdependent mapping andthe spectrum of V (x) = x2 + i

√gx3

The article [t10/034] contains an analysis ofseveral summation methods for divergent se-ries and, in particular, elaborates on an originalmethod introduced by Seznec and Zinn-Justin,called OrderDependent Mapping (ODM). The
















articles [t10/236] and [t10/238] apply the ODMmethod to a detailed study of the ground stateenergy of the non-Hermitian Hamiltonian corre-sponding to the potential x2+i

√gx3 with g > 0.

This Hamiltonian is PT symmetric, that is, it isinvariant under a simultaneous transformationx 7→ −x and complex conjugation. In 1992,Bessis and Zinn-Justin had conjectured that thespectrum of such a Hamiltonian is real. Thisproblem has then generated much interest, inparticular because it appears in some integrablemodels. The conjecture has since been provenas well as the Borel and Padé summability ofthe perturbative expansion. However, interest-ing problems remained concerning level crossing(complex PT symmetric Hamiltonians do notexperience level repulsion) and the precise re-lation with another PT symmetric Hamiltonianwith potential ivx + ix3, v real. In [t10/236] itis shown that the ODM method applied to theexpansion in powers of g allows a precise nu-merical determination of the coecients of thelarge g expansion. In [t10/238] the large g ex-pansion is used to determine the small v expan-sion. The location of the rst level crossing isdetermined, and shown to correspond to a spon-taneous breaking of the PT symmetry (collab.with U.D. Jentschura).

A.24 Zeta functions over zeros ofzeta functions (A. Voros)

The survey monograph [t09/085] covers theproperties of several kinds of zeta functions builtover the zeros ρ of the Riemann zeta functionζ(x) =

∑∞k=1 k

−x (or more generally, over thezeros of L-functions, Dedekind and Selberg zetafunctions).

Those second-generation zeta functions,called superzeta functions for brevity, aremainly:∑ρ

(ρ+t−1/2)−s,∑ρ

[ρ(1−ρ)+t2−1/4

]−s/2(summing over all the zeros; if restricted to theupper half-plane zeros instead, the leftmost sumyields a superzeta function of the third kind,which is more singular but also described in thebook).

Similar in structure to the Hurwitz zeta func-tion ζ(s, t) =

∑∞n=0(n+t)−s, the superzeta func-

tions have surprisingly many explicit, yet largelyoverlooked properties, which are surveyed inan accessible and synthetic manner, to be ul-timately compiled in some twenty tables. Nobook whatsoever had previously addressed thistopic in analytic number theory. Concretely, this

handbook should serve users of symmetric sumsover the Riemann zeros or their generalizations.More generally, it aims at reviving the inter-est of number theorists and complex analyststoward those somewhat neglected functions, onthe 150th anniversary of Riemann's work on thezeta function named after him.

Bibliography[t07/068] F. David, C. Hagendorf, and K.J.

Wiese. A growth model for RNA sec-ondary structures. J. Stat. Mech., P04008,(2008), arXiv:0711.3421.

[t07/075] I. Bena, C-W. Wang, and N.P.Warner. Plumbing the Abyss: Black RingMicrostates. JHEP, 0807, 019, (2008),arXiv:0706.3786.

[t07/104] B. Eynard. Recursion between Mum-ford volumes of moduli spaces. (2007),arXiv:0706.4403.

[t07/118] B. Eynard and N. Orantin. Topolog-ical expansion and boundary conditions.JHEP, 0806, 037, (2008), arXiv:0710.0223.

[t07/121] U. Moschella and R. Schaeer. Quan-tum Theory on Lobatchevski Spaces.Class. Quantum Grav., 24, 35713602,(2007), arXiv:0709.2795.

[t07/126] M.B. Green, J.G. Russo, and P. Van-hove. Low energy expansion of the four-particle genus-one amplitude in type II su-perstring theory. JHEP, 0802, 020, (2008),arXiv:0801.0322.

[t07/134] D. Belov, C. Hull, and R. Mi-nasian. T-duality, Gerbes and LoopSpaces. (2007), arXiv:0710.5151.

[t07/135] P. Camara and M. Graña. No-scalesupersymmetry breaking vacua and softterms with torsion. JHEP, 0802, 017,(2008), arXiv:0710.4577.

[t07/136] F. Saueressig. Recent results in four-dimensional non-perturbative string the-ory. volume 110 of J. Phys.: Conf. Ser.,102010, (2008), arXiv:0710.4931. Inter-national Europhysics Conference on HighEnergy Physics (EPS-HEP2007), Manch-ester, England, 2007-07-19/2007-07-25.

[t07/143] R. Yu, H. Saleur, and Haas . Entan-glement Entropy in the Two-DimensionalRandom Transverse Field Ising Model.Phys. Rev. B, 77, 140402(R), (2008),arXiv:0709.3840.

















[t07/154] P.F. Machado and F. Saueressig.Renormalization group ow of f(R)-gravity. Phys. Rev. D, 77, 124045, (2008),arXiv:0712.0445.

[t07/163] J. Bouttier and E. Guitter. Statis-tics of geodesics in large quadrangula-tions. J. Phys. A, 41, 145001, (2008),arXiv:0712.2160.

[t07/166] C. Candu and H. Saleur. A latticeapproach to the conformal OSp(2S+2|2S)supercoset sigma model. Part I: Algebraicstructures in the spin chain. The Braueralgebra. Nucl. Phys. B, 808, 441486,(2009), arXiv:0801.0430.

[t07/167] C. Candu and H. Saleur. A lattice ap-proach to the conformal OSp(2S+2|2S) su-percoset sigma model. Part II: The bound-ary spectrum. Nucl. Phys. B, 808, 487524, (2009), arXiv:0801.0444.

[t07/170] S. Aumaître, K. Mallick, andF. Pétrélis. Eects of the low frequen-cies of noise on On-O intermittency.J. Stat. Phys., 123, 909927, (2006),arXiv:0707.2456.

[t07/188] J.-E. Bourgine, K. Hosomichi, I.K.Kostov, and Y. Matsuo. Scattering ofLong Folded Strings and Mixed Correla-tors in the Two-Matrix Model. Nucl. Phys.B, 795, 243276, (2008), arXiv:0709.3912.

[t07/204] M. Bauer, D. Bernard, and K. Kytölä.LERW as an example of o-critical SLEs.J. Stat. Phys., 132, 721754, (2008),arXiv:0712.1952.

[t07/210] P. Di Francesco and R. Kedem. Proofof the combinatorial Kirillov-Reshetikhinconjecture. Int. Math. Res. Not., 2008,rnn006, (2008), arXiv:0710.4415.

[t07/212] K. Mallick. Anomalous diusionin a random nonlinear oscillator due tohigh frequencies of the noise. (2007),arXiv:0710.4063.

[t07/224] P. Di Francesco and P. Zinn-Justin.Quantum Knizhnik-Zamolodchikov equa-tion: reecting boundary conditions andcombinatorics. J. Stat. Mech., P12009,(2007), arXiv:0709.3410.

[t07/225] U.D. Jentschura, A. Surzhykov,M. Lubasch, and J. Zinn-Justin. Struc-ture, Time Propagation and DissipativeTerms for Resonances. J. Phys. A, 41,095302, (2008), arXiv:0711.1073.

[t07/228] J.L. Jacobsen. Exact enumeration ofHamiltonian circuits, walks, and chains intwo and three dimensions. J. Phys. A, 40,1466714678, (2007).

[t08/007] I.K. Kostov, D. Serban, and D. Volin.Functional BES equation. JHEP, 0808,101, (2008), arXiv:0801.2542.

[t08/013] P. Desrosiers. Duality in random ma-trix ensembles for all β. Nucl. Phys. B,817, 224251, (2009), arXiv:0801.3438.

[t08/017] N. Gromov, S. Schafer-Nameki, andP. Vieira. Quantum Wrapped GiantMagnon. Phys. Rev. D, 78, 026006, (2008),arXiv:0801.3671.

[t08/018] N.E.J. Bjerrum-Bohr and P. Vanhove.Explicit Cancellation of Triangles in One-loop Gravity Amplitudes. JHEP, 0804,065, (2008), arXiv:0802.0868.

[t08/019] P.A. Grassi and P. Vanhove. Higher-loop amplitudes in the non-minimal purespinor formalism. JHEP, 0905, 089,(2009), arXiv:0903.3903.

[t08/026] B. Eynard. Large N expansion ofconvergent matrix integrals, holomorphicanomalies, and background independence.JHEP, 0903, 003, (2009), arXiv:0802.1788.

[t08/027] G. Biroli, J.-P. Bouchaud, andM. Potters. The Student ensemble ofcorrelation matrices: eigenvalue spec-trum and Kullback-Leibler entropy. ActaPhys. Pol. B, 38, 40094026, (2007),arXiv:0710.0802.

[t08/032] C. Normand. Modal versus energystability analysis of kinematic dynamos incylindrical congurations. Phys. Fluids,20, 084105, (2008).

[t08/033] I. Bena, N. Bobev, and N.P. Warner.Spectral Flow, and the Spectrum of Multi-Center Solutions. Phys. Rev. D, 77,125025, (2008), arXiv:0803.1203.

[t08/044] B. Duplantier and I.A. Binder. Har-monic measure and winding of randomconformal paths: A Coulomb gas perspec-tive. Nucl. Phys. B, 802 [FS], 494513,(2008), arXiv:0802.2280.

[t08/047] B. Duplantier and S. Sheeld.Liouville Quantum Gravity and KPZ.Invent. math. (submitted), (2008),arXiv:0808.1560.

























[t08/051] T. Bargheer, N. Beisert, and N. Gro-mov. Quantum Stability for the Heisen-berg Ferromagnet. New J. Phys., 10,103023, (2008), arXiv:0804.0324.

[t08/055] S. Nonnenmacher and E. Schenck.Resonance distribution in open quan-tum chaotic systems. Phys. Rev. E, 78,045202(R), (2008), arXiv:0803.1075.

[t08/056] B. Eynard. All order asymptotic ex-pansion of large partitions. J. Stat. Mech.,P07023, (2008), arXiv:0804.0381.

[t08/057] N.E.J. Bjerrum-Bohr and P. Vanhove.Absence of Triangles in Maximal Super-gravity Amplitudes. JHEP, 0810, 006,(2008), arXiv:0805.3682.

[t08/072] B. Eynard and A. Prats-Ferrer. Topo-logical expansion of the chain of matrices.JHEP, 0907, 096, (2009), arXiv:0805.1368.

[t08/075] I. Bena, N. Bobev, C. Ruef, andP. Warner. Entropy Enhancement andBlack Hole Microstates. Phys. Rev. Lett.,105, 231301, (2010), arXiv:0804.4487.

[t08/078] J. Bouttier and E. Guitter. Thethree-point function of planar quadrangu-lations. J. Stat. Mech., P07020, (2008),arXiv:0805.2355.

[t08/081] M. Bergère and B. Eynard. Someproperties of angular integrals. J. Phys.A, 42, 265201, (2009), arXiv:0805.4482.

[t08/094] N. Gromov. Generalized ScalingFunction at Strong Coupling. JHEP, 0811,085, (2008), arXiv:0805.4615.

[t08/100] M.B. Green, J.G. Russo, and P. Van-hove.Modular properties of two-loop max-imal supergravity and connections withstring theory. JHEP, 0807, 126, (2008),arXiv:0807.0389.

[t08/104] S.Y. Alexandrov, B. Pioline, F. Sauer-essig, and S. Vandoren. Linear Pertur-bations of Hyperkähler Metrics. Lett.Math. Phys., 87, 225265, (2009),arXiv:0806.4620.

[t08/109] J.L. Jacobsen and H. Saleur. Ex-act valence bond entanglement entropyand probability distribution in theXXX spin chain and the Potts model.Phys. Rev. Lett., 100, 087205, (2008),arXiv:0711.3391.

[t08/111] J.P. Keating, S. Nonnenmacher,M. Novaes, and M. Sieber. On theresonance eigenstates of an open quantumbaker map. Nonlinearity, 21, 25912624,(2008), arXiv:0806.1678.

[t08/112] S. Marmi, P. Moussa, and J.-C.Yoccoz. Ane interval exchange mapswith a wandering interval. Proc. Lon-don Math. Soc., 100, 639669, (2010),arXiv:0805.4737.

[t08/115] S.Y. Alexandrov, B. Pioline, F. Sauer-essig, and S. Vandoren. Linear pertur-bations of quaternionic metrics. Com-mun. Math. Phys., 296, 353403, (2010),arXiv:0810.1675.

[t08/118] M. Graña, R. Minasian, M. Petrini,and D. Waldram. T-duality, General-ized Geometry and Non-Geometric Back-grounds. JHEP, 0904, 075, (2009),arXiv:0807.4527.

[t08/121] N. Gromov and P. Vieira. The all loopAdS4/CFT3 Bethe ansatz. JHEP, 0901,016, (2009), arXiv:0807.0777.

[t08/128] N. Gromov and P. Vieira. TheAdS4/CFT3 algebraic curve. JHEP, 0902,040, (2009), arXiv:0807.0437.

[t08/129] N. Gromov and V. Mikhaylov. Com-ment on the Scaling Function in AdS4x CP3. JHEP, 0904, 083, (2009),arXiv:0807.4897.

[t08/130] N. Gromov, S. Schafer-Nameki, andP. Vieira. Ecient precision quantizationin AdS/CFT. JHEP, 0812, 013, (2008),arXiv:0807.4752.

[t08/133] S. Fishman, A. Iomin, and K. Mallick.Asymptotic localization of stationarystates in the nonlinear Schroedinger equa-tion. Phys. Rev. E, 78, 066605, (2008),arXiv:0807.5005.

[t08/135] F. David, M. Dukes, T. Jonsson, andS. Stefansson. Random tree growth byvertex splitting. J. Stat. Mech., P04009,(2009), arXiv:0811.3183.

[t08/140] B. Eynard and O. Marchal. Topo-logical expansion of the Bethe ansatz,and non-commutative algebraic geometry.JHEP, 0903, 094, (2009), arXiv:0809.3367.

























[t08/152] M. Bauer, D. Bernard, andT. Kennedy. Conditioning SchrammLoewner evolutions and loop erasedrandom walks. J. Math. Phys., 50,043301, (2009), arXiv:0806.2246.

[t08/156] S.D. Badger, N.E.J. Bjerrum-Bohr,and P. Vanhove. Simplicity in the Struc-ture of QED and Gravity Amplitudes.JHEP, 0902, 038, (2009), arXiv:0811.3405.

[t08/159] F. David and M. Bauer. Anotherderivation of the geometrical KPZ rela-tions. J. Stat. Mech., P03004, (2009),arXiv:0810.2858.

[t08/164] B. Eynard and M. Mariño. Aholomorphic and background indepen-dent partition function for matrix mod-els and topological strings. (2008),arXiv:0810.4273.

[t08/182] J. Bouttier and E. Guitter. Con-uence of geodesic paths and separat-ing loops in large planar quadrangula-tions. J. Stat. Mech., P03001, (2009),arXiv:0811.0509.

[t08/185] J. Evslin and R. Minasian. Topol-ogy Change from (Heterotic) Narain T-Duality. Nucl. Phys. B, 820, 213236,(2009), arXiv:0811.3866.

[t08/189] B. Eynard and N. Orantin. Topologi-cal recursion in enumerative geometry andrandom matrices. J. Phys. A, 42, 293001,(2009), arXiv:0811.3531.

[t08/193] J.-E. Bourgine and K. Hosomichi.Boundary operators in the O(n) andRSOS matrix models. JHEP, 0901, 009,(2009), arXiv:0811.3252.

[t08/196] M. Bertola and O. Marchal. Thepartition function of the two-matrixmodel as an isomonodromic tau-function.J. Math. Phys., 50, 013529, (2009),arXiv:0809.1598.

[t08/203] S. Alexandrov, B. Pioline, F. Sauer-essig, and S. Vandoren. D-instantonsand twistors. JHEP, 0903, 044, (2009),arXiv:0812.4219.

[t08/211] I. Bena, N. Bobev, C. Ruef, and N.P.Warner. Supertubes in Bubbling Back-grounds: Born-Infeld Meets Supergravity.JHEP, 0907, 106, (2009), arXiv:0812.2942.

[t08/247] A. Ayyer and D. Zeilberger. A bijec-tional attack on the Razumov-Stroganovconjecture. (2009), arXiv:0812.0447.

[t08/252] J. Evslin and R. Minasian. Topolog-ical strings live on attractive manifolds.(2008), arXiv:0804.0750.

[t08/253] A. Butti, D. Forcella, L. Martucci,R. Minasian, M. Petrini, and A. Zaaroni.On the geometry and the moduli space ofβ-deformed quiver gauge theories. JHEP,0807, 53, (2008), arXiv:0712.1215.

[t08/255] P. Di Francesco and R. Kedem. Q-systems as cluster algebras II: Cartan ma-trix of nite type and the polynomial prop-erty. Lett. Math. Phys., 89, 183216,(2008), arXiv:0803.0362.

[t08/256] P. Di Francesco and R. Kedem. Q-systems, Heaps, Paths and Cluster Posi-tivity. Commun. Math. Phys., 293, 727802, (2008), arXiv:0811.3027.

[t08/272] J. Bros, H. Epstein, and U. Moschella.Particle decays and stability on the de Sit-ter universe. Ann. Henri Poincaré, 11,611658, (2010), arXiv:0812.3513.

[t08/277] U. Moschella and R. Schaeer. Anote on canonical quantization of eldson a manifold. JCAP, 0902, 33, (2009),arXiv:0802.2447.

[t08/297] J. Camps, R. Emparan, P. Figueras,S. Giusto, and A. Saxena. Black Ringsin Taub-NUT and D0-D6 interactions.JHEP, 0902, 021, (2009), arXiv:0811.2088.

[t08/306] J.L. Jacobsen. Unbiased samplingof globular lattice proteins in three di-mensions. Phys. Rev. Lett., 100, 118102,(2008).

[t09/012] D. Benedetti, P.F. Machado, andF. Saueressig. Asymptotic safetyin higher-derivative gravity. Mod.Phys. Lett. A, 24, 22332241, (2009),arXiv:0901.2984.

[t09/013] E. Schenck. Weyl laws for par-tially open quantum maps. Ann. Inst.Henri Poincaré (A), 10, 711747, (2009),arXiv:0811.3134v2.

[t09/015] M. Bergère and B. Eynard. De-terminantal formulae and loop equations.(2009), arXiv:0901.3273.

























[t09/020] I. Bena, Gianguido Dall'Agata,S. Giusto, C. Ruef, and N.P. Warner.Non-BPS Black Rings and Black Holesin Taub-NUT. JHEP, 0906, 015, (2009),arXiv:0902.4526.

[t09/022] R. Minasian, D. Andriot, andM. Petrini. Flux backgrounds fromTwists. JHEP, 0912, 028, (2009),arXiv:0903.0633.

[t09/024] D. Benedetti, P.F. Machado, andF. Saueressig. Taming perturbative di-vergences in asymptotically safe gravity.Nucl. Phys. B, 824, 168191, (2010),arXiv:0902.4630.

[t09/025] A. Ayyer. Towards a human proof ofGessel's conjecture. J. Integer Sequences,12, 09.4.2, (2009), arXiv:0902.2329v1.

[t09/033] B. Duplantier and S. Sheeld. Du-ality and KPZ in Liouville Quantum Gra-vity. Phys. Rev. Lett., 102, 150603, (2009),arXiv:0901.0277.

[t09/036] O. Bernardi, B. Duplantier, andP. Nadeau. A Bijection between well-labelled positive paths and matchings.Séminaire Lotharingien de Combinatoire,B63e, 113, (2010), arXiv:0903.5379.

[t09/039] M. Graña, J. Louis, A. Sim, andD. Waldram. E7(7) formulation of N=2backgrounds. JHEP, 0907, 104, (2009),arXiv:0904.2333.

[t09/041] J.-E. Bourgine. Boundary chang-ing operators in the O(n) matrix model.JHEP, 0909, 020, (2009), arXiv:0904.2297.

[t09/044] D. Volin. The 2-loop generalized scal-ing function from the BES/FRS equation.(2009), arXiv:0812.4407.

[t09/049] K. Mallick. Inuence of the noise spec-trum on the anomalous diusion in a sto-chastic system. Phys. Rev. E, 80, 011124,(2009).

[t09/050] B. Eynard. A Matrix model for planepartitions. J. Stat. Mech., P10011, (2009),arXiv:0905.0535.

[t09/052] S. Nonnenmacher and M. Zworski.Semiclassical resolvent estimates in chao-tic scattering. Appl. Math. Res. Express,2009, abp003, (2009), arXiv:0904.2986.

[t09/055] G. Borot, B. Eynard, M. Mulase, andB. Safnuk. A matrix model for simple Hur-witz numbers, and topological recursion.(2009), arXiv:0906.1206.

[t09/066] S. Alexandrov and F. Saueressig.Quantum mirror symmetry and twistors.JHEP, 0909, 108, (2009), arXiv:0906.3743.

[t09/068] J.L. Jacobsen and H. Saleur. Bound-ary chromatic polynomial. J. Stat. Phys.,132, 707719, (2008), arXiv:0803.2665.

[t09/071] J. Dubail, J.L. Jacobsen, and H. Sa-leur. Conformal two-boundary loop modelon the annulus. Nucl. Phys. B [FS], 813,430459, (2009), arXiv:0812.2746.

[t09/072] Y. Ikhlef, J.L. Jacobsen, and H. Sa-leur. A Temperley-Lieb quantumchain with two- and three-site interac-tions. J. Phys. A, 42, 292002, (2009),arXiv:0901.4685.

[t09/073] J. Dubail, J.L. Jacobsen, and H. Sa-leur. Conformal boundary conditions inthe critical O(n) model and dilute loopmodels. Nucl. Phys. B, 827, 457502,(2010), arXiv:0905.1382.

[t09/079] D. Volin. Minimal solution of theAdS/CFT crossing equation. J. Phys. A,42, 372001, (2009), arXiv:0904.4929.

[t09/081] D. Volin. From the mass gap at largeN to the non-Borel-summability in O(3)and O(4) sigma-models. Phys. Rev. D, 81,105008, (2010), arXiv:0904.2744.

[t09/085] A. Voros. Zeta functions over zeros ofzeta functions. Springer, (2010).

[t09/086] N. Berkovits, M.B. Green, J.G. Russo,and P. Vanhove. Non-renormalization con-ditions for four-gluon scattering in super-symmetric string and eld theory. JHEP,0911, 063, (2009), arXiv:0908.1923.

[t09/092] N.E.J. Bjerrum-Bohr, P.H.Damgaard, and P. Vanhove. Mini-mal Basis for Gauge Theory Amplitudes.Phys. Rev. Lett., 103, 161602, (2009),arXiv:0907.1425.

[t09/101] B. Eynard, M. Mulase, and B. Safnuk.The Laplace transform of the cut-and-join equation and the Bouchard-Mariñoconjecture on Hurwitz numbers. (2009),arXiv:0907.5224.


























[t09/109] R. Minasian, M. Petrini, and A. Zaf-faroni. New families of interpolatingtype IIB backgrounds. JHEP, 1004, 080,(2010), arXiv:0907.5147.

[t09/113] I. Bena, S. Giusto, C. Ruef, and N.P.Warner. Multi-Center non-BPS BlackHoles - the Solution. JHEP, 0911, 032,(2009), arXiv:0908.2121.

[t09/116] M. Bergère and B. Eynard. Universalscaling limits of matrix models, and (p,q)Liouville gravity. (2009), arXiv:0909.0854.

[t09/130] I. Bena, S. Giusto, C. Ruef, andN.P. Warner. A (Running) Bolt forNew Reasons. JHEP, 0911, 089, (2009),arXiv:0909.2559.

[t09/131] E. Schenck. Energy decay for thedamped wave equation under a pressurecondition. (2009), arXiv:0909.2093v1.

[t09/132] M. Bauer, D. Bernard, and L. Can-tini. O-Critical SLE(2) and SLE(4): aField Theory Approach. J. Stat. Mech.,P07037, (2009), arXiv:0903.1023.

[t09/137] I. Bena, S. Giusto, C. Ruef, andN.P. Warner. Supergravity Solutions fromFloating Branes. JHEP, 1003, 047, (2010),arXiv:0910.1860 [hep-th].

[t09/138] J. Bouttier and E. Guitter. Dis-tance statistics in quadrangulations witha boundary, or with a self-avoidingloop. J. Phys. A, 42, 465208, (2009),arXiv:0906.4892.

[t09/143] B. Vicedo. Hamiltonian dynamics andthe hidden symmetries of the AdS5 x S5

superstring. JHEP, 1001, 102, (2010),arXiv:0910.0221.

[t09/156] A. Ayyer. A Natural Bijection be-tween Permutations and a Family of De-scending Plane Partitions. Eur. J. Comb.,31, 17851791, (2010), arXiv:0909.4732.

[t09/160] G. Borot and B. Eynard. Enumera-tion of maps with self avoiding loops andthe O(n) model on random lattices of alltopologies. J. Stat. Mech. (submitted),(2010), arXiv:0910.5896.

[t09/163] P. Desrosiers and B. Eynard. Super-matrix models, loop equations, and dual-ity. (2009), arXiv:0911.1762.

[t09/175] L. Chekhov, B. Eynard, and O. Mar-chal. Topological expansion of the Betheansatz, and quantum algebraic geometry.(2009), arXiv:0911.1664.

[t09/185] C. Normand. Finite gap eects onthe instability of stratied circular Cou-ette Flow. Eur. J. Mech. B, Fluids, 29,192200, (2010).

[t09/186] J.-E. Bourgine, K. Hosomichi, andI.K. Kostov. Boundary transitions ofthe O(n) model on a dynamical lattice.Nucl. Phys. B, 882, 462499, (2010),arXiv:0910.1581.

[t09/193] C. Candu, Mitev V., Quella T.,H. Saleur, and V. Schomerus. TheSigma Model on Complex Projective Su-perspaces. JHEP, 1002, 015, (2010),arXiv:0908.0878.

[t09/194] C. Candu, J.L. Jacobsen, N. Read,and H. Saleur. Universality classes ofpolymer melts and conformal sigma mod-els. J. Phys. A, 43, 142001, (2010),arXiv:0908.1081.

[t09/195] H. Saleur and B. Pozsgay. Scatteringand duality in the 2 dimensional OSP(2|2)Gross Neveu and sigma models. J. Phys.C, 6, 41, (2009), arXiv:0910.0637.

[t09/196] B. Eynard and N. Orantin. Geo-metrical interpretation of the topologicalrecursion, and integrable string theories.(2009), arXiv:0911.5096.

[t09/221] G. Giecold. Finite-Temperature Frac-tional D2-Branes and the DeconnementTransition in 2+1 Dimensions. JHEP,1003, 109, (2010), arXiv:0912.1558.

[t09/233] P. Di Francesco and R. Kedem. Q-system Cluster Algebras, Paths and To-tal Positivity. SIGMA, 6, 014(36 pages),(2010), arXiv:0906.3421.

[t09/234] P. Di Francesco and N.Y. Reshetikhin.Asymptotic shapes with free bound-aries. Commun. Math. Phys. (submitted),(2010), arXiv:0908.1630.

[t09/235] P. Di Francesco and R. Kedem. Pos-itivity of the T-system cluster algebra.Electr. J. Combin., 16(1), R140, (2009),arXiv:0908.3122.

[t09/236] P. Di Francesco and R. Kedem. Dis-crete non-commutative integrability: the


























proof of a conjecture by M. Kontsevich.Int. Math. Res. Not., 2 March 2010, 024,(2010), arXiv:0909.0615.

[t09/237] I. Bena, M. Graña, and N. Halmagyi.On the Existence of Meta-stable Vacuain Klebanov-Strassler. JHEP (to appear),(2011), arXiv:0912.3519.

[t09/269] J. Bros, H. Epstein, M. Gaudin,U. Moschella, and V. Pasquier. Triangu-lar invariants, three-point functions andparticle stability on the de Sitter uni-verse. Commun. Math. Phys., 295, 261288, (2010), arXiv:0901.4223.

[t09/271] N. Bobev and C. Ruef. The Nutsand Bolts of Einstein-Maxwell Solutions.JHEP, 1001, 124, (2010), arXiv:0912.0010.

[t09/281] J. Dubail, J.L. Jacobsen, and H. Sa-leur. Exact solution of the anisotropicspecial transition in the O(n) model in2D. Phys. Rev. Lett., 103, 145701, (2009),arXiv:0909.2949.

[t09/282] Y. Ikhlef, J.L. Jacobsen, and H. Sa-leur. The Z2 staggered vertex model andits applications. J. Phys. A, 43, 225201,(2010), arXiv:0911.3003.

[t09/283] D. Volin. Quantum integrability andfunctional equations. PhD thesis, (2009),arXiv:1003.4725. Université Paris-Sud 11,2009-09-25.

[t09/286] N. Gromov. Integrability in AdS/CFTcorrespondence: quasi-classical analysis.J. Phys. A, 42, 254004, (2009).

[t09/290] B. Duplantier. A Rigorous Perspec-tive on Liouville Quantum Gravity and theKPZ Relation, 529561. Oxford UniversityPress, (2009).

[t09/291] B. Duplantier. Liouville QuantumGravity and the KPZ Relation: A Rigor-ous Perspective. In XVIth InternationalCongress on Mathematical Physics, 5685.World Scientic Publishing Co., (2010).ICMP09, Prague, 2009-08-03/2009-08-08.

[t09/297] U. Moschella and R. Schaeer. Quan-tum elds on curved spacetimes and anew look at the Unruh eect. volume1132 of AIP Conf. Proc., 303332, (2009),arXiv:0904.3751.

[t09/307] U.D. Jentschura, A. Surzhykov, andJ. Zinn-Justin. Generalized Nonanalytic

Expansions, PT-Symmetry and Large-Order Formulas for Odd AnharmonicOscillators. SIGMA, 5, 005, (2009),arXiv:0901.1858.

[t09/308] U.D. Jentschura, A. Surzhykov, andJ. Zinn-Justin. Unied Treatment of Evenand Odd Anharmonic Oscillators of Ar-bitrary Degree. Phys. Rev. Lett., 102,011601, (2009), arXiv:0901.4964.

[t09/326] N. Bobev, N. Halmagyi, K. Pilch, andP. Warner. Holographic, N=1 Supersym-metric RG Flows on M2 Branes. JHEP,0909, 043, (2009), arXiv:0901.2736.

[t09/327] N. Halmagyi. Non-geometric Back-grounds and the First Order String SigmaModel. (2011), arXiv:0906.2891.

[t09/328] A. Kashani-Poor and D. Cassani. Ex-ploiting N=2 in consistent coset reduc-tions of type IIA. (2011), arXiv:0901.4251.

[t09/336] J.L. Jacobsen and F. Alet. The semi-exible fully-packed loop model and inter-acting rhombus tilings. Phys. Rev. Lett.,102, 145702, (2009).

[t10/001] M.B. Green, J.G. Russo, and P. Van-hove. Automorphic properties of low en-ergy string amplitudes in various dimen-sions. Phys. Rev. D, 81, 086008, (2010),arXiv:1001.2535.

[t10/006] S. Giusto, J Morales, and R. Russo.D1D5 microstate geometries from stringamplitudes. JHEP, 1003, 119, (2010),arXiv:0912.2270.

[t10/012] M.B. Green, J.G. Russo, and P. Van-hove. String theory dualities and super-gravity divergences. JHEP, 1006, 075,(2010), arXiv:1002.3805.

[t10/020] J. Bouttier and E. Guitter. Dis-tance statistics in quadrangulations withno multiple edges and the geometry ofminbus. J. Phys. A, 43, 205207, (2010),arXiv:1002.2552.

[t10/021] J. Dubail, J.L. Jacobsen, and H. Sa-leur. Conformal eld theory at centralcharge c=0: a measure of the indecompos-ability (b) parameters. Nucl. Phys. B, 834,399422, (2010), arXiv:1001.1151.

[t10/022] D. Andriot, E. Goi, R. Minasian,and M. Petrini. Supersymmetry break-ing branes on solvmanifolds and de Sitter
























vacua in string theory. JHEP, 1105, 028,(2011), arXiv:1003.3774.

[t10/023] N.E.J. Bjerrum-Bohr and P. Vanhove.Monodromy and Kawai-Lewellen-Tye Re-lations for Gravity Amplitudes. (2010),arXiv:1003.2396.

[t10/024] E. Guitter. Distance statistics inlarge toroidal maps. J. Stat. Mech., 2010,P04018, (2010), arXiv:1003.0372.

[t10/026] B. Vicedo. The classical R-matrix ofZ4-graded supercoset sigma-models. Lett.Math. Phys. (submitted), (2010).

[t10/029] B. Eynard, A. Kashani-Poor, andO. Marchal. A matrix model for the topo-logical string I: Deriving the matrix model.(2010), arXiv:1003.1737.

[t10/030] N.E.J. Bjerrum-Bohr, P.H.Damgaard, T. Sondergaard, and P. Van-hove. Monodromy and Jacobi-likeRelations for Color-Ordered Amplitudes.JHEP, 1006, 003, (2010), arXiv:1003.2403.

[t10/034] J. Zinn-Justin. Summation of di-vergent series: Order-dependent map-ping. Appl. Numer. Math, (2010),arXiv:1001.0675.

[t10/035] U.D. Jentschura, A. Surzhykov, andJ. Zinn-Justin. Multi-Instantons and Ex-act Results III: Unied Description of theResonances of Even and Odd AnharmonicOscillators. Ann. Phys., 325, 11351172,(2010), arXiv:1001.3910.

[t10/036] U.D. Jentschura and J. Zinn-Justin.Calculation of the Characteristic Func-tions of Anharmonic Oscillators. Appl.Numer. Math, (2010), arXiv:1001.4313.

[t10/039] M.B. Green, S.D. Miller, J.G. Russo,and P. Vanhove. Eisenstein series forhigher-rank groups and string theory am-plitudes. Commun. Numb. Theor. Phys.(to appear), (2010), arXiv:1004.0163.

[t10/042] D. Serban. Integrability and theAdS/CFT correspondence. J. Phys. A, 44,124001, (2010), arXiv:1003.4214.

[t10/045] P. Vanhove. The critical ultravio-let behaviour of N=8 supergravity ampli-tudes. (2010), arXiv:1004.1392.

[t10/055] S. Nonnenmacher, J. Sjöstrand, andM. Zworski. From open quantum systems

to open quantum maps. Commun. Math.Phys., 304, 148, (2010), arXiv:1004.3361.

[t10/056] C. Hagendorf, D. Bernard, andM. Bauer. The Gaussian free eldand SLE(4) on doubly connected do-mains. J. Stat. Phys., 140, 126, (2010),arXiv:1001.4501.

[t10/074] A. Alexandrov. Matrix Mod-els for Random Partitions. (2010),arXiv:1005.5715.

[t10/079] C. Normand. Inuence of a multi-plicative noise on the threshold of helicaldynamo. Geophys. Astrophys. Fluid Dyn.,105, 90108, (2011).

[t10/081] I. Bena, N. Bobev, S. Giusto, C. Ruef,and N.P. Warner. An Innite-DimensionalFamily of Black-Hole Microstate Geome-tries. (2010), arXiv:1006.3497.

[t10/093] G. Aldazabal, E. Andres, P. Camara,and M. Graña. U-dual uxes and General-ized Geometry. (2010), arXiv:1007.5509.

[t10/099] B. Eynard, A. Kashani-Poor, andO. Marchal. A matrix model for the topo-logical string II: The spectral curve andmirror geometry. (2010), arXiv:1007.2194.

[t10/119] P. Di Francesco and R. Kedem.Noncommutative integrability, paths andquasi-determinants. Adv. Math. (submit-ted), (2010), arXiv:1006.4774.

[t10/125] I.K. Kostov and N. Orantin. CFTand topological recursion. JHEP, 11, 056,(2010), arXiv:1006.2028.

[t10/130] J. Manschot. Wall-crossing ofD4-branes using ow trees. Adv.Theor. Math. Phys. (to appear), (2010),arXiv:1003.1570.

[t10/132] I. Bena, G. Giecold, M. Graña,N. Halmagyi, and F. Orsi. Supersym-metric Consistent Truncations of IIB onT(1,1). (2010), arXiv:1008.0983.

[t10/134] F. David. A general and solvable ran-dom matrix model for spin decoherence. J.Stat. Mech., Volume 2011, P01001, (2010),arXiv:1009.1282.

[t10/135] J. Bouttier and E. Guitter. Pla-nar maps and continued fractions. Com-mun. Math. Phys. (submitted), (2010),arXiv:1007.0419.


























[t10/137] G. Borot, B. Eynard, S.N. Majum-dar, and C. Nadal. Large deviations ofthe maximal eigenvalue of random matri-ces. (2010), arXiv:1009.1945.

[t10/138] K. Bringmann and J. Manschot.From sheaves on P2 to a generalizationof the Rademacher expansion. (2010),arXiv:1006.0915.

[t10/142] J. Bros, E. De Micheli, and G.A.Viano. Nonlocal potentials and com-plex angular momentum theory. Ann.Henri Poincaré, 11, 659764, (2010),arXiv:0912.2902.

[t10/145] N.E.J. Bjerrum-Bohr, P.H.Damgaard, T. Sondergaard, andP. Vanhove. The Momentum Kernelof Gauge and Gravity Theories. (2010),arXiv:1010.3933.

[t10/146] A. Alexandrov. Cut-and-Join opera-tor representation for Kontsewich-Wittentau-function. (2010), arXiv:1009.4887.

[t10/154] L. Chekhov, B. Eynard, and O. Mar-chal. Topological expansion of β-ensemblemodel and quantum algebraic geome-try in the sectorwise approach. (2010),arXiv:1009.6007.

[t10/159] M. Beccaria, M. Kreuzer, andA. Puhm. Counting charged mass-less states in the (0, 2) heteroticCFT/geometry connection. JHEP,1101, 077, (2011), arXiv:1010.4564.

[t10/160] I Melnikov and R. Minasian. Heteroticsigma-models with N=2 space-time super-symmetry. (2010).

[t10/161] J.T. Liu and R. Minasian. Computing1/N2 corrections in AdS/CFT. (2010).

[t10/166] G. Borot and B. Eynard. Tracy-Widom GUE law and symplectic invari-ants. (2010), arXiv:1011.1418.

[t10/169] I. Bena, G. Giecold, and N. Hal-magyi. The Backreaction of Anti-M2Branes on aWarped Stenzel Space. (2010),arXiv:1011.2195.

[t10/174] I. Bena, G. Giecold, M. Graña, andN. Halmagyi. On The Inaton Poten-tial From Antibranes in Warped Throats.(2010), arXiv:1011.2626.

[t10/177] W. Staessens and B. Vercnocke. Lec-tures on Scattering Amplitudes in StringTheory. (2010), arXiv:1011.0456.

[t10/187] G. Borot and B. Eynard. The asymp-totic expansion of Tracy-Widom GUElaw and symplectic invariants. (2010),arXiv:1012.2752.

[t10/191] L. Krapivsky P. and K. Mallick. Diu-sion and Multiplication in Random Media.J. Stat. Mech., (2010), arXiv:1011.6276.

[t10/223] B. Duplantier and S. Sheeld.Schramm-Loewner Evolution and Li-ouville Quantum Gravity. (2010),arXiv:1012.4800.

[t10/231] P. Di Francesco. The solution ofthe Ar T-system for arbitrary bound-ary. Electr. J. Combin., 17, R89, (2010),arXiv:1002.4427.

[t10/232] P. Di Francesco. Discrete integrablesystems, positivity, and continued fractionrearrangements. Lett. Math. Phys., 96,299324, (2011), arXiv:1009.1911.

[t10/234] S. Marmi, P. Moussa, and J.-C. Yoc-coz. Linearization of Generalized IntervalExchange Maps. (2010), arXiv:1003.1191.

[t10/236] J. Zinn-Justin and U.D. Jentschura.Order-dependent mappings: strong cou-pling behaviour from weak couplingexpansions in non-Hermitian theories.J. Math. Phys., 51, 072106, (2010),arXiv:1006.4748.

[t10/238] J. Zinn-Justin and U.D. Jentschura.Imaginary cubic perturbation: numericaland analytic study. J. Phys. A, 43, 425301,(2010), arXiv:1006.5303.

[t10/245] N. Halmagyi. Missing Mirrors: TypeIIA Supergravity on the Resolved Coni-fold. (2011), arXiv:1003.2121.

[t10/246] N. Bobev, N. Halmagyi, K. Pilch,and P. Warner. Supergravity Instabilitiesof Non-Supersymmetric Quantum CriticalPoints. Class. Quantum Grav., 27, 5013,(2011), arXiv:1006.2546.

[t10/247] M. Guica and A. Strominger. Micro-scopic Realization of the Kerr/CFT Cor-respondence. JHEP, 1102, 010, (2010),arXiv:1009.5039.


























[t10/248] J. Raeymaekers, D.V.d. Bleeken, andB. Vercnocke. Chronology protection andthe stringy exclusion principle. (2011),arXiv:1011.5693.

[t10/258] J. Bouttier. Enumeration ofmaps. Oxford University Press, (2011),arXiv:1104.3003.

[t10/276] A. Bedini and J.L. Jacobsen. A tree-decomposed transfer matrix for computingexact Potts model partition functions forarbitrary graphs. J. Phys. A, 43, 385001,(2010).

[t10/277] J.L. Jacobsen. Demixing of com-pact polymers chains in three dimensions.Phys. Rev. E, 82, 051802, (2010).

[t10/278] J.L. Jacobsen. Bulk, surface and cor-ner free energy series for the chromaticpolynomial on the square and triangularlattices. J. Phys. A, 43, 315002, (2010).

[t10/279] J.L. Jacobsen and J. Salas. Is theve-ow conjecture almost false? (2010),arXiv:1009.4062.

[t10/283] I.K. Kostov. Matrix models as con-formal eld theories: genus expansion.Nucl. Phys. B, B837, 221238, (2010),arXiv:0912.2137 [hep-th].

[t11/014] G Aldazabal, D. Marques, C.A.Nunez, and A. Rosabal. On Type IIBmoduli stabilization and N = 4, 8 super-gravities. (2011), arXiv:1101.5954.

[t11/017] N. Gromov, D. Serban, I. Shen-derovich, and D. Volin. Quantum foldedstring and integrability: from nite sizeeects to Konishi dimension. (2011),arXiv:1102.1040.

[t11/019] I. Bena, G. Giecold, M. Graña,N. Halmagyi, and S Massai. On Meta-stable Vacua and the Warped DeformedConifold: Analytic Results. (2011),arXiv:1102.2403.

[t11/035] F. David. The importance of beingreversible. (2011), arXiv:1103.3454.

[t11/045] B. Eynard. Intersection numbers ofspectral curves. (2011).

[t11/047] P. Di Francesco and R. Kedem.The solution of the quantum A1 T-system for arbitrary boundary. (2011),arXiv:1102.5552.

[t11/048] R.E. Behrend, P. Di Francesco, andP. Zinn-Justin. On the weighted enu-meration of Alternating Sign Matricesand Descending Plane Partitions. (2011),arXiv:1103.1176.

[t11/052] C. Normand. Threshold shift of he-lical dynamo induced by stochastic owuctuations. (2011).

[t11/054] J. Dubail, J.L. Jacobsen, and H. Sa-leur. Critical exponents of domain walls inthe two-dimensional Potts model. (2011),arXiv:1008.1216.

[t11/055] J. Dubail, J.L. Jacobsen, and H. Sa-leur. Bulk and boundary critical be-haviour of thin and thick domain walls inthe two-dimensional Potts model. (2011),arXiv:1010.1700.

[t11/056] R. Bondesan, J.L. Jacobsen, andH. Saleur. Edge states and confor-mal boundary conditions in super spinchains and super sigma models. (2011),arXiv:1101.4361.

[t11/057] R. Vasseur, J.L. Jacobsen, and H. Sa-leur. Indecomposability parameters in chi-ral Logarithmic Conformal Field Theory.(2011), arXiv:1103.3134.

[t11/065] I. Bena, S. Giusto, and C. Ruef. ABlack Ring with two Angular Momenta inTaub-NUT. (2011), arXiv:1104.0016.

[t11/066] N. Halmagyi, M. Petrini, and A. Zaf-faroni. Non-Relativistic Solutions ofN=2 Gauged Supergravity. (2011),arXiv:1102.5740.

[t11/068] S. El-Showk, Y. Nakayama, andS. Rychkov. What Maxwell Theory ind 6= 4 teaches us about scale and confor-mal invariance. (2011), arXiv:1101.5385.

[t11/069] S. El-Showk and K. Papadodimas.Emergent Spacetime and HolographicCFTs. (2011), arXiv:1101.4163.

[t11/078] J. Manschot. The Betti numbersof the moduli space of stable sheaves ofrank 3 on P2. Lett. Math. Phys., (2011),arXiv:1009.1775.

[t11/080] J. Manschot, B. Pioline, and A. Sen.Wall-Crossing from Boltzmann Black HoleHalos. (2011), arXiv:1011.1258.

[t11/081] J. Manschot. BPS invariants ofN=4 gauge theory on a surface. (2011),arXiv:1103.0012.




























[t11/082] J. Manschot, B. Pioline, and A. Sen.A xed point formula for the index ofmulti-centered N=2 black holes. (2011),arXiv:1103.1887.

[t11/086] P.V. Bushlanov, A.M. Gainutdinov,and I.Yu. Tipunin. Kazhdan-Lusztigequivalence and fusion of Kac modulesin Virasoro logarithmic models. (2011),arXiv:1102.0271.

[t11/100] A. Alexandrov, A. Mironov, A. Mo-rozov, and S. Natanzon. Integrability ofHurwitz Partition Functions. I. Summary.(2011), arXiv:1103.4100.

[t11/105] A. Ayyer, R. Cori, and D. Gouyou-Beauchamps. Monotone trianglesand 312 Pattern Avoidance. (2011),arXiv:1101.1666.

[t11/134] A. Brini, B. Eynard, and M. Mariño.Torus knots and mirror symmetry. (2011),arXiv:1105.2012.

[t11/143] S. Nonnenmacher, J. Sjöstrand, andM. Zworski. Fractal Weyl law foropen quantum chaotic maps. (2011),arXiv:1105.3128.

[t11/144] S. Nonnenmacher. Spectral prob-lems in open quantum chaos. (2011),arXiv:1105.2457.








CHAPTERB

Cosmology and particle physics

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

B.1 Physics of the early universe . . . . . . . . . . . . . . . . . . . . . . . . 82

B.1.1 Primordial non-Gaussianities . . . . . . . . . . . . . . . . . . . . . . . . 82

B.1.2 Nonlinear perturbations . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

B.1.3 Scalar tachyons in the de Sitter universe . . . . . . . . . . . . . . . . . . 82

B.1.4 A new lattice code to study preheating . . . . . . . . . . . . . . . . . . . 82

B.1.5 Gravitational waves from primordial phase transitions . . . . . . . . . . 82

B.1.6 Cosmic magnetic elds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

B.1.7 DBI cosmic strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

B.2 CMB physics beyond linear order . . . . . . . . . . . . . . . . . . . . 84

B.2.1 Recombination era . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

B.2.2 Late-time eects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

B.3 Formation of large-scale structures . . . . . . . . . . . . . . . . . . . . 84

B.3.1 Resummation schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

B.3.2 Combined models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

B.3.3 Burgers dynamics as a toy model . . . . . . . . . . . . . . . . . . . . . . 86

B.3.4 Phenomenological models for halo mass functions and bias . . . . . . . 86

B.3.5 Reconstruction of the large-scale velocity eld . . . . . . . . . . . . . . . 87

B.4 Observation of primordial non-Gaussianities in large-scale structures 87

B.5 Dark energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

B.5.1 Building quintessence models . . . . . . . . . . . . . . . . . . . . . . . . 87

B.5.2 Impact on large-scale structures . . . . . . . . . . . . . . . . . . . . . . . 87

B.5.3 Large-scale structure growth in modied gravity models . . . . . . . . . 88

B.5.4 Time drift of cosmological redshifts and its variance . . . . . . . . . . . 88

B.5.5 Stars within the Chaplygin gas . . . . . . . . . . . . . . . . . . . . . . . 88

B.6 Weak lensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

B.6.1 Second-order eects in the cosmic shear . . . . . . . . . . . . . . . . . . 88

B.6.2 Sensitivity to primordial non-Gaussianities . . . . . . . . . . . . . . . . 88

B.7 Collider signatures of new physics . . . . . . . . . . . . . . . . . . . . 89

B.7.1 The top quark as a window on new physics . . . . . . . . . . . . . . . . 89

B.7.2 Composite Higgs physics . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

B.8 Flavour physics and neutrinos . . . . . . . . . . . . . . . . . . . . . . . 90

B.8.1 Flavour models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

B.8.2 Leptogenesis and lepton avour violation . . . . . . . . . . . . . . . . . 91

B.9 Supersymmetry and string phenomenology . . . . . . . . . . . . . . . 92

B.9.1 Supersymmetry breaking and its mediation . . . . . . . . . . . . . . . . 92

73


B.9.2 Non-minimal supersymmetric extensions of the Standard Model . . . . . 92

B.9.3 Phenomenology of string models . . . . . . . . . . . . . . . . . . . . . . 93

B.10 The electroweak phase transition . . . . . . . . . . . . . . . . . . . . . 93

B.10.1 The nature of the electroweak phase transition and its cosmological im-prints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

B.10.2 Bubble growth in rst-order phase transitions . . . . . . . . . . . . . . . 94

B.11 Dark matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

B.11.1 Dark matter phenomenology and model-building . . . . . . . . . . . . . 94

B.11.2 Dark matter and Grand Unication . . . . . . . . . . . . . . . . . . . . 95

B.11.3 Extra-dimensional dark matter . . . . . . . . . . . . . . . . . . . . . . . 95

B.11.4 A top quark - dark matter connection . . . . . . . . . . . . . . . . . . . 95

B.11.5 Dark matter interpretation of cosmic ray data . . . . . . . . . . . . . . . 96

B.11.6 Neutrino cosmology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

B.12 Particle physics models for the early Universe . . . . . . . . . . . . . 97

B.12.1 Ination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

B.12.2 Supersymmetry breaking and ination . . . . . . . . . . . . . . . . . . . 97

B.12.3 Dark energy and modied gravity . . . . . . . . . . . . . . . . . . . . . 97

B.13 Gauge theory amplitudes . . . . . . . . . . . . . . . . . . . . . . . . . . 98

B.13.1 Symmetries of scattering amplitudes in gauge theories . . . . . . . . . . 98

B.13.2 New techniques for scattering amplitudes . . . . . . . . . . . . . . . . . 99

B.13.3 NLO amplitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

B.13.4 SUSY particle production . . . . . . . . . . . . . . . . . . . . . . . . . . 101

B.14 Jet algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

B.14.1 Optimal jet radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

B.14.2 Jets in heavy ion collisions . . . . . . . . . . . . . . . . . . . . . . . . . 102

B.14.3 FastJet package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

B.15 Color Glass Condensate . . . . . . . . . . . . . . . . . . . . . . . . . . 102

B.15.1 Angular ordering in the evolution towards saturation . . . . . . . . . . . 102

B.15.2 BFKL physics in hadron-hadron collisions . . . . . . . . . . . . . . . . . 102

B.15.3 Geometric scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

B.15.4 Global ts to HERA data . . . . . . . . . . . . . . . . . . . . . . . . . . 103

B.15.5 Gluon saturation in forward observables . . . . . . . . . . . . . . . . . . 104

B.15.6 CGC calculations for the Electron Ion Collider . . . . . . . . . . . . . . 104

B.15.7 Saturation scale from Wilson line correlators . . . . . . . . . . . . . . . 104

B.15.8 Factorization in the saturated regime . . . . . . . . . . . . . . . . . . . . 104

B.15.9 Multiplicity in nucleus-nucleus collisions . . . . . . . . . . . . . . . . . . 105

B.15.10Two gluon correlations at large rapidity . . . . . . . . . . . . . . . . . . 105

B.15.11Schwinger mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

B.15.12Thermal equilibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

B.15.13Collisional meson dissociation . . . . . . . . . . . . . . . . . . . . . . . . 106

B.16 Central diractive processes . . . . . . . . . . . . . . . . . . . . . . . . 106

B.17 Gauge-gravity duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

B.17.1 Parton picture at strong coupling . . . . . . . . . . . . . . . . . . . . . . 107

B.17.2 Langevin dynamics and jet quenching at strong coupling . . . . . . . . . 107

B.17.3 Heavy quark energy loss at strong coupling . . . . . . . . . . . . . . . . 107

B.17.4 A lattice test of the strong coupling hypothesis . . . . . . . . . . . . . . 108

B.17.5 Mesons in a strongly coupled plasma . . . . . . . . . . . . . . . . . . . . 108

B.17.6 Radiation at strong coupling: the quest for string uctuations . . . . . . 108

B.17.7 Viscosity of the QGP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

B.17.8 Early time dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

B.17.9 High energy bounds on N=4 SYM amplitudes . . . . . . . . . . . . . . . 109

B.17.10Brane cosmology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Cosmology and particle physics 75

B.17.11Hadrons in AdS/QCD models . . . . . . . . . . . . . . . . . . . . . . . . 109

B.18 Relativistic hydrodynamics . . . . . . . . . . . . . . . . . . . . . . . . 109

B.18.1 Flow extraction methods . . . . . . . . . . . . . . . . . . . . . . . . . . 109

B.18.2 The four lowest harmonics . . . . . . . . . . . . . . . . . . . . . . . . . . 110

B.18.3 Long-range correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

B.18.4 HBT interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

B.18.5 Exact solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

B.19 QFT at nite temperature . . . . . . . . . . . . . . . . . . . . . . . . . 111

B.19.1 Heavy quarks in a quark-gluon plasma . . . . . . . . . . . . . . . . . . . 111

B.19.2 Exact renormalization group . . . . . . . . . . . . . . . . . . . . . . . . 112

B.19.3 Random matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

B.19.4 Lattice QCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

B.19.5 Boundary eective theory . . . . . . . . . . . . . . . . . . . . . . . . . . 113

B.20 Cold baryonic matter at high density and compact stars . . . . . . . 114

B.20.1 Half-skyrmion matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

B.20.2 Dilatons and the repulsive core . . . . . . . . . . . . . . . . . . . . . . . 114

B.20.3 Holographic dual QCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

B.20.4 Neutron stars and black holes . . . . . . . . . . . . . . . . . . . . . . . . 115

B.21 Theoretical nuclear physics . . . . . . . . . . . . . . . . . . . . . . . . 115

B.21.1 Theory of fusion and ssion . . . . . . . . . . . . . . . . . . . . . . . . . 115

B.21.2 Theory of density functionals . . . . . . . . . . . . . . . . . . . . . . . . 115

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Introduction

The research activities of the Particle Physics and Cosmology group of the IPhTcover a broad range of topics in theoretical cosmology, astroparticle physics, particlephysics beyond the Standard Model, quantum chromodynamics and nuclear physics.

Cosmology is a very active research topic at the IPhT and our activities in thiseld range from studies of the early Universe (e.g., inationary scenarios) to workson the large-scale structures observed in the present Universe.

A rst major topic of modern cosmology is the generation during an early in-ationary era of the primordial uctuations that seeded the large-scale structures(such as galaxies) that we observe today. In particular, while the simplest single-eld scenarios predict almost-Gaussian initial uctuations, alternative models (e.g.,multield ination) can give rise to signicant non-Gaussianities. This topic ofprimordial non-Gaussianities has become a very active subject in the community,with the upcoming increasingly precise observations (e.g., the current Planck mis-sion), as it gives a sensitive probe of early Universe physics. On a rst side, wehave computed the nonlinear contributions to higher-order correlations that arisein single-eld models, and we have for instance uncovered new contributions to thefour-point function. On a second side, we have studied the non-Gaussianities gener-ated in multield models, including both gravity and non-gravity induced couplings.

Another important probe of the early Universe would be the detection of gravita-tional waves generated by primordial phase transitions. We have developed analyt-ical models to evaluate the stochastic background of gravitational waves generatedby the collision of broken phase bubbles and by the associated magnetohydrody-namical turbulence. We have thus shown that the space interferometer LISA coulddetect this background for electroweak symmetry breaking scenarios leading to astrongly rst order phase transition.


A related topic is the possible generation of magnetic seeds in the primordialUniverse, which could explain the ubiquitous magnetic elds that we observe todayon cosmological scales. We have built a detailed model for the evolution of magneticelds in the primordial plasma and obtained new constraints on generation mech-anisms. We have also considered its impact on the Cosmic Microwave Background(CMB) anisotropies.

A second important subject of current cosmology is the study of the CMB ani-sotropies. In relation with the upcoming Planck data and the study of primordialnon-Gaussianities, it has become necessary to go beyond linear order, to keep pacewith observational precision and to distinguish primordial signals from late-timenonlinear eects. We have performed a series of works to study such eects and wehave computed the main contributions at second order to the CMB uctuations,as well as the full second-order bispectrum, by a consistent implementation of theBoltzmann equation. This is a long-term project that aims at building a CMBcode up to second order, which will be quite valuable for the community. On theother hand, we have also computed secondary eects, due for instance to the timedependence of the potentials along the line of sight and to lensing distortions.

A third major topic is the study of the formation of large-scale structures. In-deed, from the distribution of galaxies and clusters we can obtain complementaryconstraints on the background cosmology (such as the behavior of the dark energycomponent) and primordial uctuations. This again requires precise predictions,up to 1% on weakly nonlinear scales, which has led to a recent surge of activityin perturbation theory, motivated by the development of dedicated wide eld sur-veys. Indeed, it is possible to improve over the standard perturbative approachby implementing resummation schemes, which provide better controlled and moreaccurate predictions. Several approaches have been proposed and developed at theIPhT, and can already be applied to non-Gaussian initial conditions or combinedto phenomenological models to cover the highly nonlinear regime. This is again along-term project that aims at building accurate and fast methods, in order to reachthe accuracy required by future observations (e.g., Euclid).

On a more theoretical side, we have also performed a series of works to study asimplied toy model, the adhesion model, where exact or well-controlled resultscan be derived, to shed light on the nonlinear aspects of the dynamics and thebehavior of such resummations. In particular, we have been able to explain thedierent behaviors found in the Eulerian and Lagrangian frameworks.

In relation with the topic of primordial non-Gaussianities, we have also studied indetail the signature of this primordial signal in the low-redshift large-scale structures,using both analytical tools and numerical simulations. In particular, we have esti-mated the constraints that can be obtained on scale-dependent non-Gaussianities,which had not been much studied yet.

A fourth important subject is the understanding of the dark energy component,which is one of the major puzzles of theoretical physics. This is a very active topic inthe community, which has led to the development of major observational projects,such as the future space mission Euclid. We have studied quintessence modelswith a vanishing sound speed, where the dark energy component clusters and canaect the formation of large-scale structures. More generally, we have estimated theconstraints on the dark energy equation of state that can be derived from the CMB.

Finally, in the eld of weak lensing, which is a long-held topic at the IPhT,


we have presented the rst computation up to second order of the cosmic shear,including all relativistic eects and without relying on small-angle approximations.We have also estimated the sensitivity of weak lensing observables on primordialnon-Gaussianities.

The cosmology section of this chapter gathers contributions from 8 permanentresearchers, F. Bernardeau, C. Caprini, P. Valageas, F. Vernizzi, who specialize oncosmology, and P. Brax, J. Bros, V. Pasquier, G. Servant, who also contribute toother chapters; and 3 postdocs, C. Bonvin (who left in September 2010), Z. Huang(who arrived in October 2010), E. Sefusatti (who arrived in January 2009). Thegroup also has 1 current PhD student, N. van de Rijt.

Particle physics beyond the Standard Model is a very active research subject inSaclay, where many of its aspects are studied, from electroweak symmetry breakingto astroparticle physics. These activities take place in a particularly rich experimen-tal context: the Large Hadron Collider (LHC) at CERN has started to explore theterascale and is going to shed light on fundamental questions regarding the buildingblocks of matter and their relative interactions; neutrino and avour physics experi-ments are providing us with complementary information about the avour structureof the physics relevant at high energies; a variety of astroparticle physics experimentsare constraining the properties of dark matter and may help us, in conjunction withthe LHC, to identify its nature; and nally, cosmological observations are deliveringmore and more accurate information about cosmological parameters.

An important part of our research activities in physics beyond the StandardModel aims at identifying the dynamics of electroweak symmetry breaking throughits signatures at the LHC. Since the top quark has a large Yukawa coupling to theHiggs boson, top physics is a privileged place where to look for such signatures. Forinstance, a generic prediction of models in which the Higgs boson arises as a pseudo-Goldstone boson is the existence of fermionic partners of the top quark, whoseproduction at the LHC has been studied in detail. Model-independent approachesbased on eective eld theories were developed in order to interpret the anomalouslylarge forward-backward asymmetry in tt production measured at the Tevatron, andto assess the sensivity of top quark collider observables to new physics. Simulationsof specic observables like four-top production were also performed. Deviationsfrom the standard Higgs mechanism can also be probed in the Higgs sector itself,and this was demonstrated for double Higgs production, or by searching for spin-1 resonances of the electroweak gauge bosons, which are characteristic of manyalternative scenarios of electroweak symmetry breaking.

Another very active line of research at the IPhT is the physics of avour andCP violation, in which indirect signals of physics beyond the Standard Model mayappear. A rst question of interest is the origin of the quark and lepton massand mixing patterns, which could be related to the mechanism that suppressesnew physics contribution to avour- and CP-violating observables. The disparitybetween the large lepton mixing and the small CKM mixing angles in the quarksector, for instance, could be explained by discrete avour symmetries, and this hasbeen addressed both in the context of Grand Unication and of strong electroweaksymmetry breaking scenarios. The eciency of the avour symmetry and wavefunction renormalization approaches in suppressing supersymmetric avour violationwere compared. We also pursued the study of the implications of massive neutrinos,


within the supersymmetric seesaw mechanism, for the baryon asymmetry of theUniverse and for avour- and CP-violating processes. In particular, a connectionbetween leptogenesis and CP violation at low energy was found in some GrandUnied models. Finally, the possibility of observing new fermions generically presentin low-scale avour gauge theories has been studied.

A traditionally strong activity in Saclay is the study of supersymmetric modelsand their phenomenology. Supersymmetry breaking and its mediation to the observ-able sector has been investigated in the framework of gauge-mediated supersymme-try breaking. It was demonstrated that radiative corrections can stabilize the super-symmetry breaking vacuum while allowing for sizable gaugino masses, thus evadinga well-known problem of gauge mediation. Also, unconventional superpartner spec-tra with well-dened gaugino mass ratios were shown to arise in the presence of anunderlying Grand Unied Theory. Various aspects of non-minimal supersymmetricmodels and string compactications were studied, such as four-fermion interactionsarising in intersecting D-brane models, or the occurrence of singlet extensions of theminimal supersymmetric standard model in heterotic orbifolds.

A much strengthened line of research at the IPhT in the last few years is the onein the domain of astroparticle physics and particle cosmology, i.e. at the intersectionbetween particle physics beyond the Standard Model and cosmology or astrophysics.In this line lie the works performed on the electroweak phase transition, dark matter,dark energy and ination models.

The dynamics of the electroweak phase transition in the early Universe is verysensitive to the actual mechanism of electroweak symmetry breaking. It is wellknown that it cannot be rst order within the Standard Model, as successful elec-troweak baryogenesis would require, but the situation can be dierent in alternativescenarios. We have studied the dynamics of electroweak bubble nucleation when theHiggs boson emerges as a composite bound state from a strongly interacting sector,and showed that the associated signal in gravity waves can be large. From a model-independent perspective, we have studied the hydrodynamics of bubble growth in arst-order phase transition, which is relevant both for electroweak baryogenesis andfor the size of the gravity wave signal resulting from bubble collisions.

Dark matter constitutes most of the matter content of the Universe, as a num-ber of cosmological and astrophysical observations now conrm. However, little isknown about its nature and it has not been directly detected yet. Many new particlecandidates for dark matter, coming from various extensions of the Standard Model,have been identied and studied over the last decade. Within this broad context,the research performed at the IPhT has moved along two main axes. The rst oneis the exploration of dark matter phenomenology in specic models. This includesthe investigation of Minimal Dark Matter, a new model proposed by us a few yearsago, whose predictions for direct and indirect dark matter experiments have beenprecisely computed; and the study of new dark matter candidates from Grand Uni-ed Theories, warped extra dimensions and from a strongly-interacting electroweaksymmetry breaking sector. The second axis is the model-independent analysis ofrecent cosmic ray observations in terms of dark matter and the identication of thecorresponding constraints. It was shown in particular that the lack of associatedsignals impose very strong restrictions on dark matter interpretations of chargedcosmic ray data.

With the advent of the era of precision cosmology, there has been a renewed


interest in particle physics models for the early Universe, and the IPhT has activelyparticipated in this eort over the past four years. We have studied a certain numberof inationary models and their consequences for preheating and the formation ofcosmic strings. We have also analysed possible inationary scenarios within theIntriligatorSeibergShih framework of metastable supersymmetry breaking. Theaccelerated expansion of the Universe may be due to cosmologically coupled scalarelds, such as chameleons. Motivated by this, we investigated the possibility ofobserving scalar eld models coupled to matter in laboratory experiments, and ourwork prompted a large body of experimental activity. Following our original workin 2002 and 2004, we have also studied the modication of the growth of structuresinduced by the presence of a cosmologically coupled scalar eld.

The beyond the Standard Model section of this chapter gathers contributions from7 permanent researchers: P. Brax, M. Chemtob (emeritus), M. Cirelli, C. Grojean,S. Lavignac, C. Savoy (emeritus), G. Servant; 5 postdocs: M. Frigerio (2005-2009),F. Iocco (2008-2009), J.-M. No (2009-2011), A. Sil (2006-2009), G. Zaharijas (2009-2011); and 6 PhD students, E. Cluzel, C. Delaunay, P. Hosteins, S. Mariadassou,P. Panci and J. Parmentier, who defended their theses in September 2011, October2008, September 2007, December 2011, March 2011 and July 2011, respectively.

The study of strong interactions is a very active and diverse activity at theIPhT. Our activities cover a broad spectrum of research topics, ranging from nuclearphysics to studies of quantum chromo-dynamics in the context of searches of newphysics at the LHC.

A major thread of research in our group is the study of amplitudes in gaugetheories, mostly QCD but also supersymmetric variants such as the N = 4 super-symmetric Yang-Mills theory that can be employed as a laboratory for studyingnew approaches. A common theme in these studies is the use of hidden symmetriesand structures satised by these amplitudes, that can be employed to bypass thestandard computation techniques in terms of Feynman diagrams. In recent years,this has led to a breadth of new methods for eciently computing amplitudes inQCD (typically, amplitudes with many externals legs, possibly up to NLO). Our ac-tivity on this subject ranges from the study of formal aspects of these symmetries,the development of new on-shell techniques for computing one-loop amplitudes, andthe implementation thereof in a form that can be directly used in phenomenologicalstudies.

Another related area of study is the development of new jet algorithms. Theseare important tools in the experimental study of QCD at high energy colliderssuch as the LHC in order to make the contact between perturbatively calculablecross-sections, in terms of quarks and gluons, and actual measurements that seeonly hadrons. Any suitable jet algorithm must be infrared and collinear safe. Inaddition, the very large particle multiplicity in nal states at the LHC (especiallyin heavy ion collisions) renders crucial the clustering eciency of these algorithms.We have played a central role in developing new jet algorithms, such as the kt andanti-kt algorithms, that are now used by the major collaborations at the LHC.

An important domain of research at the IPhT is the study of the Color GlassCondensate, an eective theory for the study of hadronic and nuclear wave functionsin the high energy regime, where gluon saturation eects become important. Theseeects are crucial for instance in a rst principles study of nucleus-nucleus collisions


at high energy. Our activity here covers both formal aspects that aim at developingthe formalism and justifying its applicability to high energy collisions (e.g. viafactorization theorems that relate various types of reactions), and phenomenologicalstudies whose goal is to confront the predictions of the Color Glass Condensateeective theory to experimental results at HERA, RHIC or the LHC.

There has been in the last four years some activity on central diractive produc-tion in hadronic collisions at high energy at the TEVATRON or at the LHC, whichis a very clean production channel for new particles such as the Higgs, since theycan be measured with almost no background.

The last four years have seen the appearance of new domains of application ofthe AdS/CFT correspondence (and more generally gauge-gravity dualities). Whilethese ideas were so far employed in order to study formal properties of gauge theoryamplitudes, these techniques have now made an incursion into the territory of thephenomenology of quark-gluon matter at high temperature, such as the matterproduced in heavy ion collisions. All these studies deal with QCD-like theoriesrather than QCD itself, but it is believed that some of their properties at strongcoupling are rather close to those of QCD. Thanks to these techniques, we havestudied at strong coupling questions such as the parton picture, the energy loss of aheavy quark in a plasma, the properties of meson bound states in hot matter, andthe viscosity of the quark-gluon plasma.

In heavy ion collisions at high energy, the experimental results for bulk observ-ables suggest that the quark-gluon matter produced in these collisions can be de-scribed as an almost frictionless uids in expansion and can be modelled usingrelativistic hydrodynamics. An important observation is that the nal anisotropyof the momentum of the observed particles can be related via the hydrodynamicalevolution to the initial shape anisotropies of the system. Our group has played amajor role in developing practical methods for measuring the parameters that quan-tify these anisotropies in the experimental results. A major result has also been therealization that event-by-event shape uctuations are an essential ingredient in in-terpreting these results. Our team has also worked on some more formal aspects ofrelativistic hydrodynamics, by obtaining exact solutions in some special cases.

During the last four years, there have also been some work on quantum eldtheories at nite temperature. This activity has covered several topics: the behaviorof heavy quarks in the quark-gluon plasma, the exact renormalization group andits applications, random matrices applied to the study of connement, and latticestudies of SU(3) gauge theory in three dimensions.

Another domain of study of the strong interactions group at the IPhT is that ofcold baryonic matter at high density. The equation of nuclear matter in this regimeis poorly known, and could possibly undergo a number of phase transitions, and itis of central importance in the physics of compact stars. This problem has beenaddressed by various methods: hidden local symmetry, holographic methods andgauge-gravity dualities, and topological arguments.

Theoretical nuclear physics has mainly concerned two areas in the period coveredby this report: the theory of fusion and ssion reactions, and the mathematicalfoundations of the nuclear density functional.

The strong interactions section of this chapter contains contributions from 13permanent researchers: J.-P. Blaizot, P. Brax, R. Britto, F. Gelis, B. Giraud,E. Iancu, G. Korchemsky, D. Kosower, A. Morel, J.-Y. Ollitrault, R. Peschanski,


M. Rho, G. Soyez; and from 11 postdocs: J. Albacete, E. Avsar, S. Badger, G. Di-ana,Y. Hatta, H. Johansson, M. S. Kugeratski, T. Lappi, M. Luzum, C. Marquet,E. Mirabella. During this four year period, 3 students have obtained their PhD inthe strong interaction group: G. Beuf, C. Gombeaud, C. Vergu, and 3 students havestarted a PhD: J. Laidet, L. Palhares, Z. Peng.


B.1 Physics of the early universe

B.1.1 Primordial non-Gaussianities (F.Bernardeau, F. Vernizzi)

The observation of primordial non-Gaussianitieswould be of dramatic importance for our under-standing of the inationary era, as a detection(or a tight upper bound) could constrain or ruleout many inationary models.

First, within the standard single-eld ina-tionary model, which is still consistent with cur-rent data, it has become important to studycosmological perturbations beyond linear orderto extract information from the observations,which are getting increasingly precise. This sub-ject of research has become popular under thename of primordial non-Gaussianities. In par-ticular, a large eort of the community has beendevoted to the study of higher-order correlationsin the cosmological perturbations, which pro-vide information about interactions taking placeduring ination. Using the so-called in-in (orSchwinger-Keldysh) formalism, in collaborationwith Seery and Sloth we have studied the four-point function generated during ination fromexchange of gravitons [t08/251]. This was therst worked-out example of calculation of anexchange diagram in the cosmological context.This contribution to the four-point function hadbeen previously overlooked in the literature andit is of the same order as the one coming frompurely scalar gravitational interactions.

Second, it is known that alternative mod-els of ination with multiple elds can producelarge primordial non-Gaussianities. One mech-anism is through self couplings of the elds inisocurvature directions. In [t10/038] a short re-view of this mechanism is given emphasizing thedierence of amplitude to be expected betweengravity and non-gravity induced couplings. In[t10/114], exact mathematical results are givenregarding the amplitude evolution of inducedbispectra, in case of non-gravity couplings, fordierent inationary backgrounds.

B.1.2 Nonlinear perturbations (F. Ver-nizzi)

In [t10/244] we have reviewed, by invitation ofClassical and Quantum Gravity, the covariantapproach to cosmological perturbations devel-oped in collaboration with David Langlois in aseries of papers published from 2005 to 2008.

B.1.3 Scalar tachyons in the de Sitteruniverse (J. Bros)

In collaboration with H. Epstein and U.Moschella [t10/237], we provide a construction

of a class of local and de Sitter covariant tachy-onic quantum elds, namely elds which sat-isfy a de Sitterian Klein-Gordon (K-G) equa-tion with discrete negative values of the squared-mass parameter and which have no Minkowskiancounterpart. Technically, the construction goesthrough a primitive (Krein-type) space S withindenite-metric, on which the eld only satisesan anomalous non-homogeneous K-G equa-tion. Then it is in a de Sitter invariant physicalsubspace of states with positive squared-normand nite codimension in S that the true K-Gequation is restored. This phenomenon (whichcarries some reminiscence of the Gupta-Bleulerconstruction of QED) turns out to disappearin the Minkowskian limit (i.e.the innite radiuslimit of the de Sitter hyperboloid or the van-ishing cosmological constant), but it might verywell be present in a de Sitter modelization of theearly universe with a very tiny radius.

B.1.4 A new lattice code to study pre-heating (Z. Huang)

In [t11/075] we present a new lattice code,HLattice, that studies the dynamics of scalarelds and gravity in the early universe. It diersfrom previous publicly available codes in threeaspects: (i) a much higher accuracy is achievedwith a modied 6th-order symplectic integrator;(ii) the backreaction from gravity to the dynam-ics of scalar elds is consistently included; (iii)it includes a new method to separate gravitywaves from the total metric perturbations. Weexplain that the traditional way to calculate gra-vity waves suers from a lattice eect that mixesthe scalar modes and tensor modes. Thus, someof the earlier results may be insuciently accu-rate or even wrong by an order of magnitude.

B.1.5 Gravitational waves from primor-dial phase transitions (C. Caprini,G. Servant)

First order phase transitions in the early uni-verse can give rise to a stochastic backgroundof gravitational waves (GW). Three main pro-cesses lead to the production of the GW signal:the collision of the broken phase bubbles, themagnetohydrodynamical (MHD) turbulence inthe plasma stirred by the bubble collisions, andthe magnetic elds amplied by the MHD tur-bulence. In [t07/142, t09/011, t09/121, t10/072]analytical methods have been developed to pre-dict the main features of the GW power spec-trum, starting from a description of the sourcewhich we tried to make as simple and as modelindependent as possible. In particular, [t07/142]













analyzes GW production by bubble collisions,providing a model for the bubble velocity powerspectrum based on a statistical description thatis suitable for both detonations and deagra-tions. Then, [t09/011] compares the analyticalresults with the GW spectra derived from nu-merical simulations of bubble collisions, estab-lishing that the structure of the unequal timecorrelation of the GW source and its continuityin time are fundamental for a correct determina-tion of the peak position of the GW spectrum.In [t09/121], a detailed model of the MHD tur-bulence generated by bubble collisions is pro-posed, accounting for the fact that turbulenceand magnetic elds act as sources of GW formany Hubble times after the phase transitionis completed, modeling the initial stirring phasepreceding the Kolmogorov cascade, and using arealistic power spectrum for the MHD turbu-lence. The main conclusion of these works isthat the GW signal from a rst order phase tran-sition occurring at electroweak symmetry break-ing falls into the sensitivity range of the spaceinterferometer LISA if the phase transition lastsfor about one hundredth of the Hubble time andthe energy density of the turbulent motions isabout twenty percent of the total energy densityin the universe at the phase transition time.

The advantage of building an analyticalmodel for the GW source is that the main fea-tures of the resulting GW spectrum, such as thepeak frequency, the amplitude, and the slopesboth at low and high wavenumbers, can be pre-dicted by general arguments based on the char-acteristics of the source: in particular, the struc-ture of its space and time correlation. The re-sulting spectrum depends on a few parametersdescribing the source, and can then be applied todierent specic models of the phase transition.For example, in [t10/120] the picture developedin the aforementioned analysis is applied to ahypothetical rst order QCD phase transition:the amplitude and the spectral shape of the GWare predicted, demonstrating that the signal ispotentially interesting for detection via pulsartiming arrays.

B.1.6 Cosmic magnetic elds (C. Bonvin,C. Caprini)

The observational evidence of large-scale mag-netic elds in matter structures covers nowadaysan impressive range of length scales and red-shifts: from galaxies to high-redshift quasars,from clusters and superclusters to low-densitylamentary regions. However, the origin of theseelds remains an open problem. One of the pos-

sible explanations is that they have been gen-erated in the primordial universe: primordialmagnetogenesis mechanisms have in fact the ad-vantage of providing magnetic seeds lling theentire universe, which goes in the right direc-tion to explain both the ubiquity of the observedelds and the uniformity of the measured ampli-tudes. If a primordial magnetic eld is presentin the early universe, observables such as theCMB or Nucleosynthesis can be used to inferlimits on its intensity or make predictions on itspossible detection. Very stringent upper boundson the magnetic eld intensity have been de-rived using gravitational waves at Nucleosynthe-sis, which strongly challenge some of the pro-posed generation mechanisms occurring beforeNucleosynthesis, such as primordial phase tran-sitions [t09/169, t11/064]. A detailed modelingof the magnetic eld evolution in the primordialplasma has been developed both for helical andnon-helical elds to render these bounds moreprecise and realistic [t09/169, t09/121]. Mag-netogenesis mechanisms operating after Nucle-osynthesis, mainly based on charge separation,are mostly inecient, since they rely on the pres-ence of vorticity in the primordial plasma, whichis small and dicult to generate: for example,it cannot be transferred from the metric to thematter uids at linear order purely by gravi-tational interactions [t07/156]. Therefore, thegeneral picture that can be inferred is that aprimordial magnetic eld generated by a non-causal process, such as ination, and with a redspectrum, seems to be favored as a seed for themagnetic elds observed today in structures.

The most convincing way to establishwhether such a eld is present in the primor-dial universe, would be to detect its trace in theCMB. Therefore, it is important to predict allthe eects that a magnetic eld would have onthe CMB anisotropies. For example, in [t10/071]the shape of the scalar temperature anisotropyinduced by a magnetic eld at low multipolesis analyzed in connection with the right initialconditions for the eld and the metric perturba-tions. Moreover, a magnetic eld would gener-ate non-Gaussianities in the CMB: in [t09/031]the CMB bispectrum of the scalar temperatureanisotropy is derived, and used to infer upperbounds on the magnetic eld intensity throughthe WMAP bounds on fNL.

B.1.7 DBI cosmic strings (P. Brax, C.Caprini)

In [t08/155], we study cosmic string congu-rations in a model that extends the standard













Abelian-Higgs one with a non-linear Dirac-Born-Infeld (DBI) action for the kinetic term. Theprole of the cosmic strings is studied numeri-cally and it is demonstrated that the core is nar-rower than that of Abelian-Higgs strings. More-over, it is found that the corresponding actionis smaller than in the standard case suggest-ing that the formation of DBI-cosmic stringscould be favored in brane models. The stringsolutions are non-pathological everywhere in pa-rameter space, and DBI cosmic strings are nolonger BPS: rather they have positive bindingenergy, suggesting that, when they meet, twoDBI strings will not bind with the correspond-ing formation of a junction. Hence, a network ofDBI strings is likely to behave as a network ofstandard cosmic strings.

B.2 CMB physics beyond linearorder

In order to constrain the primordial non-Gaussianities discussed in Sect. B.1.1 from ob-servations of the CMB (or other probes), wemust rst be able to predict with a goodaccuracy the contributions to observed non-Gaussianities that arise from late-time nonlineareects. These may take place during the recom-bination era as well as during the late matterand dark energy dominated eras.

B.2.1 Recombination era (F. Bernardeau)

In a series of papers [t08/162, t09/244, t10/032,t10/195] written in collaboration with J.-Ph.Uzan and C. Pitrou, we have explored thephysics of mode couplings during the recombi-nation era and how they can lead to a signi-cant bispectrum in the CMB temperature eld.This is a work program that has been activelypursued by several teams and that aims at char-acterizing the intrinsic temperature and polar-ization bispectra to be expected in CMB obser-vations. These mode couplings can be viewedas a background signal against which mode cou-plings eects originating from the inationaryera can be compared.

In our rst paper, [t08/162], we identiedthe leading mechanism at play at small angularscales. We found it to be due to mode couplingsin the sub-horizon gravitational potential dom-inated by the CDM component. In fact, thosecoupling eects take place very early - even be-fore equality - and we explain how their eectscan be computed through the response functionof the photon anisotropies computed at linearorder. Using this approach, we can also esti-mate the amplitude of the CMB bispectrum on

small scales, although it is not possible to com-pute the CMB bispectrum in all congurations.To be able to do so, we derived and implementedthe set of equations consistently describing theevolution of the second-order temperature uc-tuations, e.g. including the second-order eectscontained in the Boltzmann equation. Theseinvestigations culminated in [t10/032], wherewe presented the resulting shape of the bispec-trum. There are two companion papers. One,[t09/244], stresses that at second order the pho-ton energy distribution is actually non-thermal;there is therefore a dierence between the bolo-metric temperature and the occupation num-ber temperature whose statistical properties areslightly dierent. We also present in [t10/195] adetailed mathematical derivation of how the atsky approximation can be used through control-lable expansions, including the case of bispectracomputations.

B.2.2 Late-time eects (F. Vernizzi)

As explained above, in order to interpret higher-order correlations in the cosmological data, it isimportant to develop theoretical tools that al-low us to disentangle a primordial cosmologi-cal signal from late-time physics due to gravi-tational interactions. In this context, in collab-oration with Boubekeur, Creminelli, D'Amico,and Noreña, we have calculated the three-pointfunction in the CMB anisotropies generated dur-ing the post-inationary evolution, for low mul-tipoles and in a matter dominated universe[t09/201]. In this particular limit the calcula-tion can be performed almost analytically andchecked by physical arguments. The generatedthree-point function is dominated by lensing, acontribution that was overlooked in the litera-ture, but it is below Planck sensitivity.

B.3 Formation of large-scalestructures

B.3.1 Resummation schemes (F. Bernar-deau, E. Sefusatti, P. Valageas)

The growth of large-scale structures in the Uni-verse through the amplication of small primor-dial uctuations by gravitational instability is akey ingredient of modern cosmology. This pro-cess can be used to constrain cosmological pa-rameters as well as the initial conditions. In par-ticular, some observational probes (e.g., baryonacoustic oscillations) focus on weakly nonlinearscales and require theoretical predictions for thematter power spectrum and bispectrum (i.e. thelow-order correlation functions) with an accu-racy of 1%. This has led to a renewed inter-











est in perturbation theory, since these scales arewithin the reach of perturbative approaches. In-deed, in addition to the standard perturbationtheory it is useful to build resummation schemesthat can provide increasingly accurate analyticalmethods and avoid the use of costly numericalsimulations. Several of these approaches are be-ing developed in IPhT.

The Gamma-expansion approach (RPT)

In the framework of Eulerian perturbation the-ories we have extended exact results found byCrocce and Scoccimarro to a whole family of ob-jects: the multi-point propagators. These quan-tities describe how a given mode is changed byan innitesimal variation of the amplitude of oneor a nite number of modes in the initial con-ditions. In [t08/161], we have shown that spec-tra at any order can be reconstructed from theknowledge of those objects, by glueing themtogether. This is the essence of the Γ-method(or RPT for renormalized perturbation the-ory) and this is the motivation for extensivestudies of the multi-point propagators. In thesame paper, we have also shown that the UV(i.e. short wave-mode) behavior of these objectscan indeed be explicitly computed through theresummation of a whole class of diagrams. Thisapproach proves very general. In [t10/090] wedescribe how it can be implemented in case ofnon-Gaussian initial conditions, explaining howthe Γ-expansion is modied and giving the ex-plicit expressions of the multi-point propagatorsin their UV limit.

Path-integral formulation and large-Nexpansions

In addition to the RPT approach discussedabove, many resummation schemes have beenproposed in the literature and in [t07/162] wehave tested several methods (large-N expan-sions, RPT, running with a high-k cuto)by using the simpler Zeldovich dynamics as abenchmark. We nd that most methods (ex-cept for RPT) fail to recover the relaxation ofthe matter power spectrum on highly nonlinearscales, as one goes to high orders. We also ex-plain how RPT is based on the approximationof a wide separation of scales and describes thetransport of small-scale density uctuations bylarger-scale velocity modes (sweeping eect),rather than a true relaxation due to small-scaleinteractions.

Next, in [t08/016] we have described how twolarge-N resummation schemes can be used toobtain the matter power spectrum and bispec-

trum (as well as higher-order correlations), forboth the Zeldovich and the actual gravitationaldynamics.

Eulerian versus Lagrangian propagators

A key quantity that arises in most resumma-tion schemes is the propagator, or response func-tion, that describes how uctuations propagatewith time. In the usual Eulerian framework,this propagator shows a fast decay that is gov-erned by the sweeping eect described above.In order to go beyond this eect, we have inves-tigated in [t08/160] the propagators that arisein a Lagrangian framework, since the latter areinsensitive to this sweeping eect. Applyingthe RPT approach, in the reformulation of[t07/162], we nd that this leads to a Lagrangianpropagator that no longer decays in the non-linear regime. In order to better understandthis dierence, we have studied in [t09/216]the Eulerian and Lagrangian propagators associ-ated with the one-dimensional adhesion model,based on the Burgers dynamics, where many ex-act results can be derived. We show that the Eu-lerian propagators can be expressed in terms ofthe one-point velocity probability distribution,and exhibit a strong exponential decay, whilethe Lagrangian propagators can be written interms of the halo mass function and only showa power-law decay, which is related to the thelow-mass tail of the mass function. This ex-plains these qualitatively dierent behaviors andsuggests that Lagrangian propagators are muchmore sensitive probes of small-scale relaxation.

B.3.2 Combined models (P. Valageas)

The approaches described in Sect. B.3.1, whichare based on the uid approximation and per-turbative expansions, cannot go beyond shellcrossing (where the velocity eld becomes multi-valued) and handle highly nonlinear processes.Using the Zedovich dynamics as a benchmark,and a closely related sticky model, we com-pare in [t10/170] the amplitude of perturbativeand non-perturbative terms (which we can com-pute exactly at all orders for these two sim-pler dynamics). We nd that for the standardΛCDM initial conditions the potential of per-turbative schemes is greater at higher redshift,since one can go up to order 66 of perturba-tion theory at z = 3, and to order 9 at z − 0,before non-perturbative contributions becomedominant. This further motivates the study ofresummation schemes, especially at z > 1.

For practical purposes, it is useful to ob-tain unied models that can describe all scales.










We have described in [t10/171] how to combine(resummed) perturbation theories with phe-nomenological halo models. In particular, wehave shown that the halo-model contributionscontain counterterms that had been missed inprevious works and ensure a physically mean-ingful and accurate behavior.

B.3.3 Burgers dynamics as a toy model(F. Bernardeau, P. Valageas)

Perturbative approaches only oer a partial un-derstanding of the nonlinear gravitational dy-namics while it can be dicult to distinguishintermediate physical processes from the resultsof numerical simulations. In order to go beyondthese limitations it is useful to investigate sim-pler toy models that can be fully understood andwhere exact results can be derived. They canalso serve as benchmarks for general approxima-tion schemes. This motivates the study of theadhesion model, which goes beyond the Zel-dovich dynamics by making particles cluster af-ter collisions instead of escaping to innity andthus includes some fully nonperturbative shellcrossing eects. This is also known as the Burg-ers dynamics in the uid dynamics context.

Thus, we have undertaken a series of worksto study the Burgers dynamics, paying atten-tion to issues that arise in the cosmological con-text. In [t08/199], we derive many exact prop-erties of the one-dimensional Burgers dynam-ics for the case of initial velocity elds that arealso Brownian motions. In particular, we notethat both the stable-clustering ansatz and thePress-Schechter mass function, that are widelyused in the cosmological context, happen to beexact in this case. As a by-product, we havealso derived new results for a ballistic aggrega-tion process in [t08/201].

Next, in [t09/179] we study the case of white-noise one-dimensional initial velocity eld, de-riving again exact expressions such as the den-sity power spectrum and halo mass function. Wealso discuss the generalization to other initialconditions and higher dimensions through a mul-tifractal formalism.

Then, using an asymptotic method that wehad developed in previous works on the grav-itational dynamics, we derive in [t09/180] theasymptotic velocity and density probability dis-tributions of this Burgers dynamics in the quasi-linear regime and for rare-event tails (includinghigh-mass nonlinear shocks). This applies torandom Gaussian initial conditions in arbitrarydimension, with power-law initial power-spectra,which is the case of interest for both the ad-

hesion model in cosmology and the decayingBurgers turbulence in uid dynamics.

In dimension two and higher, the Burgersdynamics can be quite complex and the veloc-ity eld does not fully dene the matter distri-bution. More precisely, one must add to theEuler equation a continuity equation and sev-eral choices are possible (that coincide outsideof the shock manifold). In [t09/250] we discussin detail how a geometrical Burgers dynamics,which can be built from the initial elds throughgeometrical constructions, provides an elegantmodel but diers from using the usual continu-ity equation. In particular, this leads to bothhalo mergings and fragmentations in dimensiongreater or equal to two, a property that wassometimes overlooked in the literature.

Finally, in [t10/173] we present a numericalstudy of this geometrical Burgers dynamics inboth one and two dimensions. We introduce anew algorithm, based on exact geometrical con-structions, that provides the exact dynamics foreach initial condition. Focusing again on ran-dom Gaussian initial conditions, with power-lawinitial spectra, we nd that many statistical in-dicators show the same qualitative properties asthose observed for 3D gravitational clustering.In particular, the mass functions obey to a largeextent the usual Press-Schechter like scaling.These results again suggest that this geometri-cal Burgers dynamics provides a useful tool tounderstand gravitational clustering.

B.3.4 Phenomenological models forhalo mass functions and bias (P.Valageas)

Two quantities that are closely related to ob-servational studies of galaxies and clusters ofgalaxies are the halo mass function and cor-relation (or bias). Most popular models forthese two statistics involve several free parame-ters that need be tted to numerical simulationsand lessen their predictive power. We have pre-sented in [t09/181] a simpler model that requiresfewer free parameters, while remaining in goodagreement with simulations, and which shouldbe more robust. We also point out the impactof halo motions on their two-point correlation.Next, we have extended this approach to non-Gaussian initial conditions in [t09/182], and tohalos dened by arbitrary density thresholds in[t10/172].












B.3.5 Reconstruction of the large-scalevelocity eld (F. Bernardeau)

It has been shown that, in a large rangeof dynamical regimes, the Monge-Ampère-Kantorovitch (MAK) reconstruction methodcan be used to recover the initial position of ob-served galaxies, and consequently their present-day 3D velocity. Such observations would bevery important for characterizing the large-scalestructure of the universe. These results were ob-tained however in ideal cases where biasing, -nite volume eects were absent. In [t07/123] weextensively study the uncertainty in the mass-to-light assignment due to incompleteness (miss-ing luminous mass tracers), and the poorly de-termined relation between mass and luminosity.We eventually show that, in the context of obser-vational data, it is possible to build a relativelyunbiased estimator of Ωm using MAK.

B.4 Observation of primordialnon-Gaussianities in large-scale structures (E. Sefusatti,P. Valageas)

Primordial non-Gaussianities may also be ob-served through their impact on large-scale struc-tures, which provide a complementary probe tothe CMB studied in Sect. B.2. Again, this re-quires accurate predictions and detailed stud-ies of perturbation theory, especially since pri-mordial non-Gaussianities are usually greater onlarge quasi-linear scales. In [t09/054] we havederived the expressions for the one-loop con-tributions in cosmological, Eulerian, perturba-tion theory to the matter bispectrum and to thegalaxy bispectrum, in presence of non-Gaussianinitial conditions. In particular, we describe thepeculiar dependence on scale and shape of thetriangular congurations of these various contri-butions to the bispectra.

Next, we have presented a detailed compari-son with numerical simulations in [t10/141]. Wend that one-loop perturbation theory providesquite accurate predictions at redshifts z > 1,and still provides a signicant improvement overtree-level computations at z = 0.

Although the primordial non-Gaussian pa-rameter fNL is often taken to be constant, ithas been shown to be scale-dependent in sev-eral models of ination with a variable speed ofsound. In [t09/321], we perform a Fisher ma-trix analysis of the bispectra of the temperatureand polarization of the CMB and derive the ex-pected constraints on the parameter nNG thatquanties the running of fNL(k) for current and

future CMB missions such as WMAP, Planckand CMBPol. On the other hand, we nd thatlarge-scale structure observations should achieveresults comparable to or even better than thosefrom the CMB, while showing some complemen-tarity due to the dierent distribution of thenon-Gaussian signal over the relevant range ofscales.

We have reviewed in [t10/140] the theoreti-cal and observational problems associated withstudies of primordial non-Gaussianity throughbispectrum measurements in the CMB andsarge-scale structures. In particular, we describecurrent results and future prospects for the de-tection of a non-vanishing primordial componentand its relation with dierent inationary mod-els.

From the observational point of view, wehave studied in [t09/183] optimized estimatorsto probe primordial non-Gaussianities, throughthe observation of the CMB or the distributionof galaxy clusters, and their cross-correlations.In particular, they compress the data associatedwith three-point correlations into one-point esti-mators that retain the sensitivity to primordialnon-Gaussianities and some scale dependence.

B.5 Dark energy

B.5.1 Building quintessence models (F.Vernizzi)

Dark energy is the cosmological component re-sponsible for the current acceleration of theUniverse. It is usually assumed to be smoothon cosmological scales. For instance, stan-dard quintessence based on a minimally cou-pled canonical scalar eld propagates uctua-tions at the speed of light, maintaining themhomogeneous within a Hubble patch. How-ever, there are theoretical motivations to con-sider quintessence models based on a scalar eldwith zero sound speed. These models can beconstructed using an eective eld theory ap-proach and have the advantage to be stable alsowhen the equation of state of dark energy is lessthan -1, that is, P/ρ < −1 [t09/202].

B.5.2 Impact on large-scale structures(C. Caprini, E. Sefusatti, F. Vernizzi)

A dark energy component with zero soundspeed would alter the evolution of structuresnot only by changing the background evolu-tion of the Universe but also by actively par-ticipating to gravitational clustering. This ismost evident in the regime where structures be-come nonlinear. In collaboration with Crem-inelli, D'Amico, Noreña, and Senatore, we have









studied this regime using the spherical collapsemodel [t09/199], showing that quintessence con-tributes to the total halo mass by a fraction thatincreases at low redshifts and is proportional tothe ratio between quintessence and dark matterenergy densities. The nonlinear regime of struc-ture formation has been further studied usingEulerian perturbation theory in [t11/007]. Inparticular, we show that the reduced bispectrumreceives sensible modications in the clusteringcase, similar to those found in the spherical col-lapse model, that can potentially be used to de-tect or rule out the model.

From the observational point of view, weinvestigate in [t08/015] the power of next-generation CMB and large-scale structure sur-veys in constraining the nature of dark energythrough the cross-correlation of the IntegratedSachs Wolfe eect and the galaxy distribution.We demonstrate that a survey which covers morethan 35% of the sky, with a median redshifthigher than 0.8, and which detects more thana few galaxies per squared arcmin, can detectthe correlated signal at a level of more than 4sigma. The constraints that such a survey canput on the nature of dark energy (through dif-ferent parametrizations of its equation of state)are then computed with a standard Fisher ma-trix analysis.

B.5.3 Large-scale structure growth inmodied gravity models (F. Bernar-deau, P. Brax)

In [t11/099] we explore the mode-coupling struc-ture and amplitude in a class of modied gra-vity models. This class of models correspondsto dilaton induced modied gravity that takesadvantage of the chameleon mechanism to passthe GR tests within the solar system. We showthat the dilaton eld introduces a whole new se-ries of coupling terms (of any order) that canbe signicant on scales of observational interest.We show that the amplitude of these eects forbispectra could be detectable - it is at few per-cents level - oering a way to discriminate amongdierent dark energy models through large-scalestructure observations.

B.5.4 Time drift of cosmological red-shifts and its variance (F. Bernar-deau)

In the context of the ELTs (Extremely LargeTelescope) scientic case, it has been claimedthat it could be possible to measure the equa-tion of state of the universe (hence to constrainthe dark energy component) from the measure-

ment of the time drift of redshifts of absorptionclouds (along the line of sight of quasars). Thismethod may however suer from large system-atics. In [t08/022] we explore the eects of pe-culiar acceleration and how it compares to theHubble acceleration.

B.5.5 Stars within the Chaplygin gas (V.Pasquier)

A simple model for the dark energy is theChaplygin gas, characterized by an equationof state of the form p ∝ −1/ρ. In [t08/188]we have studied static solutions of the Tolman-Oppenheimer-Volko equations for sphericallysymmetric objects (stars) living in a space lledwith this Chaplygin gas. Two cases were consid-ered. In the normal case all solutions (exclud-ing the de Sitter one) realize a three-dimensionalspheroidal geometry. The second case ariseswhen the modulus of the pressure exceeds theenergy density (the phantom Chaplygin gas).There is no more equator and all solutions havethe geometry of a truncated spheroid with thesame type of singularity.

B.6 Weak lensing

B.6.1 Second-order eects in the cosmicshear (F. Bernardeau, C. Bonvin, F.Vernizzi)

As for CMB observations, it is important to ob-tain accurate predictions for weak lensing ob-servables in order to put constraints on cosmol-ogy and primordial initial conditions. We havestudied in [t09/200] the cosmic shear, i.e. thecollective eect of gravitational lensing distor-tions on galaxy shapes due to the foregroundgravitational matter eld. In particular, we havecomputed the reduced cosmic shear up to secondorder in the gravitational potential without re-lying on the small-angle or thin-lens approxima-tions. This leads to new couplings in additionto the standard non-linear terms.

B.6.2 Sensitivity to primordial non-Gaussianities (E. Sefusatti)

In [t11/051] we quantitatively evaluate the im-pact of primordial non-Gaussianity onto weaklensing auto- and cross-correlation power spec-tra. We show that it is strongly suppressed byprojection eects. More generally, we point outthat the clustering of biased tracers of the three-dimensional density eld is generically more sen-sitive to non-Gaussianity than observables con-structed from projected density elds.










B.7 Collider signatures of newphysics

B.7.1 The top quark as a window on newphysics (C. Grojean, G. Servant)

The top quark being the heaviest of all the ele-mentary fermions of the Standard Model (SM),it is expected to play a special role in electroweaksymmetry breaking. It has been among the cen-tral physics topics at the Tevatron and it willremain so at the LHC during this decade. Intheories beyond the SM that provide a mech-anism for mass generation, new physics musthave a large coupling to the top quark. Itis therefore natural to use top quark observ-ables to test the mechanism responsible for elec-troweak symmetry breaking and more generallyto search for physics beyond the SM. For in-stance, the problem of the quantum stabilityof the weak scale together with current elec-troweak data provide a plausible motivation forconsidering a light Higgs emerging as a pseudo-Goldstone boson from a strongly-coupled sector.On the other hand, this approach also suggeststhat SM fermion masses should arise via mixingof elementary fermions with composite fermionsof the strong sector. In this context, the topquark is mainly a composite object while theother light SM quarks are mainly elementary. Anatural prediction is then the existence of light(. 1TeV) fermionic composite partners of thethird generation fermions, in particular the topquark. At the LHC, composite quarks can bepair-produced with a large QCD cross section.They can also be singly produced. Prospects atthe LHC for their discovery are very promising,as shown in collaboration with R. Contino. In[t07/149], we studied the pair production anddetection at the LHC of the top partners withelectric charge Q = 5/3 (T5/3) and Q = −1/3(B), that are predicted in models where theHiggs is a pseudo-Goldstone boson. The exoticT5/3 fermion, in particular, is the distinct predic-tion of a Left-Right custodial parity invariance ofthe electroweak symmetry breaking sector. Bothkinds of new fermions decay to Wt, leading toa ttWW nal state. We focussed on the goldenchannel with two same-sign leptons, and showedthat a discovery could come with less than 100pb−1 (less than 20 fb−1) of integrated luminosityfor masses M = 500GeV (M = 1TeV). In thecase of the T5/3, we presented a simple strategyfor its reconstruction in the fully hadronic decaychain. Our analysis also directly applies to thesearch of 4th generation b' quarks and is beingpursued by ATLAS and CMS.

We have also developped some model-independent approaches based on low-energy ef-fective eld theory. In [t10/302], we used topquark pair production as a probe of top-philicnon-resonant new physics. Following a low-energy eective eld theory approach, we cal-culated several key observables in top quarkpair production at hadron colliders (e.g. to-tal cross section, tt invariant mass distribution,forward-backward asymmetry, spin correlations)including the interference of the Standard Modelwith dimension-six operators. We determinedthe LHC reach in probing new physics after hav-ing taken into account the Tevatron constraints.In particular, we showed that the gluon fusionprocess gg → tt which remains largely uncon-strained at the Tevatron is aected by only onetop-philic dimension-six operator, the chromo-magnetic moment of the top quark. This opera-tor can be further constrained by the LHC dataas soon as a precision of about 20% is reached forthe total tt cross section. In [t11/128], we alsopresented the eective eld theory approach tosame-sign top pair production, in relation withthe tt forward-backward asymmetry. While ourapproach is general and model independent, itis particularly relevant to models of Higgs andtop compositeness.

With ATLAS PhD student Léa Gauthierfrom SPP, we worked on the rst detailedsimulation of four-top production at the LHC[t10/301], [t10/305]. Four-top production is aspectacular nal state and a sensitive probe ofnew physics that is relatively unconstrained byprecision measurements at LEP or resonancesearches at the Tevatron. Examples are modelswhere the top quark is composite or where a newheavy particle couples strongly or exclusively totop quarks. A study of four-top production wasalso done for a multi-TeV e+e− collider such asCLIC in [t10/300].

B.7.2 Composite Higgs physics (C. Delau-nay, C. Grojean)

Notwithstanding its simplicity, the appeal ofthe SM Higgs picture comes from its success-ful agreement with electroweak precision data,provided that the Higgs boson is rather light. Inthis regard, being an elementary scalar is not avirtue but rather a aw because of the quadraticdivergences destabilizing the Higgs mass. Itis thus tantalizing to consider the Higgs bosonas a composite bound state emerging from astrongly-interacting sector. In order to main-tain a good agreement with electroweak data,it is sucient that a mass gap separates the








Higgs resonance from the other resonances of thestrong sector. Such a mass gap can naturallyfollow from dynamics if the strongly-interactingsector possesses a global symmetry, G, spon-taneously broken at a scale f to a subgroupH, such that the coset G/H contains a fourthNambuGoldstone bosons that can be identi-ed with the Higgs boson. In these models, thephysics of the Higgs boson is determined by twoadditional parameters that depend on the globalsymmetries of the strong sector at the origin ofthe breaking of the electroweak symmetry, asshown in our previous work JHEP 0706 (2007)045. In [t10/304], we have analyzed how thesearches for the Higgs boson are aected by itsunderlying dynamics and we have evaluated thediscovery potential of the Higgs boson at theLHC. This analysis oers a promising way toprobe deviations away from the SM. However,such deviations might have various origins. Onedistinctive and genuine signature of the strongdynamics responsible for the electroweak sym-metry breaking is the growth with energy ofthe scattering amplitudes among the Goldstonebosons of the SM, i.e., the longitudinally polar-ized vector bosons as well as the Higgs bosonitself. In [t10/031], we studied the enhancementof the double Higgs production by vector bosonfusion in pp collisions.

The composite Higgs models have a naturalavour structure that easily explains the fermionmass spectrum without generating troublesomeavour changing neutral currents. This struc-ture automatically explains the alignment of themasses and mixing angles in the quark sector.However, the large mixing in the neutrino sec-tor requires additional avour symmetries. In[t08/271], we presented, in the context of mod-els of strong electroweak symmetry breaking, asimple model of lepton masses and mixing basedon the A4 non-abelian discrete symmetry withno tree-level lepton avour violation and smallloop-induced lepton avour amplitudes.

The composite Higgs models are a contin-uous interpolation between the SM and Higgs-less models, i.e., models where the longitudi-nal WW scattering amplitudes are unitarizedvia the exchange of spin-1 resonances. An in-troduction to Higgsless models has been pre-sented in [t07/217] and various alternative ap-proaches to explain the dynamics of the elec-troweak symmetry breaking have been reviewedin [t07/218] and [t09/295]. Most of the alter-native models are characterized by the existenceof massive spin-1 degrees of freedom, some of

them carrying an electric charge. In [t11/131],we studied the discovery prospect of such a W ′

at the LHC through its decays to 2 jets, Wγand WZ. In particular, we show that the decaychannelW ′ →Wγ, which is strongly suppressedin gauge models, could indicate a composite na-ture of this heavy resonance and could thus pro-vide valuable information about the true dynam-ics of the breaking of the electroweak symmetry.

C. Grojean has also edited several schooland workshop proceedings [t07/122], [t08/276],[t09/294], [t10/305], [t10/306], [t10/307].

B.8 Flavour physics and neutrinos

B.8.1 Flavour models (C. Grojean, M.Frigerio, J. Parmentier, C. Savoy)

Notwithstanding our fair knowledge of the quarkavour parameters (their masses, mixing anglesand the CKM phase) and the strong experimen-tal constraints on the leptonic ones, we haveno cogent explanation for their origin yet. Thequest for a theory of avour that would bothprovide a rationale for the measured parametersand yield testable predictions is an active eldof research.

In [t09/293], the results of the current gener-ation of avour physics experiments were sum-marised and confronted with the theoretical pre-dictions, which have greatly improved in thepast decade.

Some features of the quark and lepton massand mixing patterns suggest possible underlyingavour symmetries. In collaboration with E. Ma[t07/110], it was shown that the smallness of the1-3 lepton mixing angle and of the ratio betweenthe solar and atmospheric neutrino mass squareddierences can be understood as the departurefrom a common limit where they both vanish.We found that the simplest avour symmetrythat can correlate the values of these two param-eters is the discrete group Q8, the smallest non-abelian subgroup of SU(2). As a consequence, alower bound on the 1-3 mixing is predicted andwill be tested soon experimentally.

An important issue in avour physics is thedisparity between the large lepton mixing an-gles and the small CKM mixing in the quarksector. This problem is particularly severe inthe context of Grand Unication, where leptonsand quarks belong to the same multiplets. Incollaboration with F. Bazzocchi and S. Morisi[t08/126], we demonstrated that it is nonethelesspossible to unify all SM fermions into a unique(16,3) representation of the SO(10)×A4 group,where SO(10) is the unied gauge group and A4


















is the group of even permutations of four ob-jects, acting as a avour symmetry. Our analysisshows that tri-bi-maximal lepton mixing (thatis, tan2 θ23 = 1, tan2 θ12 = 0.5, tan2 θ13 = 0)as well as hierarchical quark and charged leptonmasses can be both explained in this frameworkand share a related origin. This represents a sig-nicant step towards a avour theory compatiblewith Grand Unication.

In collaboration with E. Dudas, G. von Gers-dor and S. Pokorski [t10/243], we comparedthe theoretical and experimental predictions oftwo classes of models addressing the fermionmass hierarchies and the avour changing neu-tral current (FCNC) problem in supersymmetry:FroggattNielsen U(1) gauged avour modelsand NelsonStrassler/extra-dimensional modelswith hierarchical quark and lepton wave func-tions. We showed that, while both approacheslead to identical predictions for the fermion massmatrices, the second class of models yields astronger suppression of FCNC eects. More-over, although at rst sight the FroggattNielsensetup is more constrained due to anomaly can-celation, imposing the unication of gauge cou-plings in the extra-dimensional case generatesconditions which precisely match the mixedanomaly constraints in the FroggattNielsen sce-nario. Finally, we provided an economical extra-dimensional realisation of the hierarchical wavefunction scenario in which the leptonic FCNCeects can be eciently suppressed due to thestrong coupling (CFT) origin of the electronmass.

Many avour models have been proposed toexplain the pattern of quark and lepton massesand mixing angles, but they are testable only ifthe avour symmetry is broken at relatively lowenergies. The intrinsic parity violation by theavour charges associated with the light quarksand leptons requires anomaly cancellation bynew heavy fermions. In [t11/122], benchmarksupersymmetric avour models have been builtand studied to argue that: i) the avour sym-metry breaking should be about three orders ofmagnitude above the higgsino mass, which isalso enough to eciently suppress avour andCP violations from higher-dimensional eectiveoperators; ii) new fermions with exotic decaysinto lighter particles are typically required atscales of the order of the higgsino mass. Theheavy quarks would be more easily producedat the LHC and could perhaps be identied bytheir decay into an energetic lepton and two jets.Actually, the (non-supersymmetric) minimal ex-

tension of the Standard Model to such a avourtheory requires the new fermions to be quasi-stable, which makes the observation of the newquarks stopped at the detector even easier.

B.8.2 Leptogenesis and lepton avourviolation (M. Frigerio, P. Hosteins, S.Lavignac)

One of the challenges extensions of the Stan-dard Model have to face is to generate dynami-cally the observed baryon asymmetry of the Uni-verse. Among the proposed mechanisms, lepto-genesis is a very attractive one since it just re-quires the addition of the heavy elds that areneeded to generate the small neutrinos massesvia the seesaw mechanism. The requirementthat leptogenesis generates the observed cos-mological baryon asymmetry thus represents anon-trivial constraint on theories that includethese ingredients, such as Grand Unied Theo-ries based on the SO(10) gauge group. In collab-oration with A. Abada and F.-X. Josse-Michaux[t08/069], we performed a detailed quantitativestudy of leptogenesis in SO(10) models witha left-right symmetric seesaw mechanism, inwhich neutrino masses arise from the exchangeof both heavy right-handed neutrinos and aheavy SU(2)L triplet. We solved numericallythe avour-dependent Boltzmann equations in-cluding the contribution of the next-to-lightestright-handed neutrino, and found that successfulleptogenesis is indeed possible in these models,while it is dicult to achieve in SO(10) modelswith a type I seesaw mechanism.

In [t08/070], in collaboration with A. Ro-manino, we investigated a particularly predic-tive leptogenesis scenario, which is realized inSO(10) models with matter elds lying both in16 and in 10 representations. In this scenario,neutrino masses originate from a triplet seesawmechanism, and the relevant CP asymmetry isdirectly related to the light neutrino mass pa-rameters. In particular, the CP violation neededfor leptogenesis is provided by the phases ofthe lepton mixing (PMNS) matrix, which canin principle be measured experimentally. Thisis to be contrasted with most leptogenesis sce-narios, in which the CP asymmetry depends onunknown high-energy parameters and is uncon-nected to low-energy CP violation. Successfulleptogenesis in this scenario requires a ratherlarge value of the yet unknown mixing angle θ13.

In a subsequent paper written in collabora-tion with L. Calibbi and A. Romanino [t09/158],we studied avour changing processes in thesame SO(10) scenario. We showed that the







raditively-induced avour violating eects arecontrolled by purely low-energy avour parame-ters (namely the CKM and PMNS matrices, to-gether with the neutrino and up quark masses),while their overall size also depends on high-energy parameters. Requiring successful lepto-genesis constrains the latter to vary within asmall range, yielding predictions for avour vi-olating processes. In particular, µ → eγ lieswithin the reach of the MEG experiment if thesuperpartner spectrum is accessible at the LHC,and the agreement between the theoretical pre-diction for the indirect CP violation parameterin the kaon system εK and its measured valuecan be improved.

B.9 Supersymmetry and stringphenomenology

B.9.1 Supersymmetry breaking and itsmediation (S. Lavignac, J. Parmen-tier)

If supersymmetry is discovered at the LHC, animportant question will be to identify the mech-anism responsible for its breaking and mediationto the observable sector. The ratios of gauginomasses will provide useful information: they arepredicted to be in the same ratios as the gaugecouplings squared in the most popular schemes,minimal gauge mediation and minimal super-gravity. Any deviation from this proportion-ality relation would signal a non-minimal me-diation mechanism. In [t08/110], [t10/097], incollaboration with E. Dudas, we studied gaugemediation scenarios in which the dominant con-tribution to messenger masses comes from theircouplings to the Higgs elds responsible for thebreaking of an underlying grand unied gaugegroup. This results in a non-standard superpart-ner spectrum whose features are mainly deter-mined by the unied gauge group and the mes-senger representations. Explicit examples in-clude spectra with an unusually light bino, whichcan even be the lightest supersymmetric particle(LSP), as well as spectra with a gluino or winoNLSP and a gravitino LSP, which lead to spe-cic signatures at the LHC. A complete, viablemodel with an explicit supersymmetry breakingsector of the IntriligatorSeibergShih type cou-pled to the messenger elds was constructed.

Gauge mediation is an attractive mechanismfor transmitting supersymmetry breaking to theobservable sector, since it automatically solvesthe supersymmetric avour problem. However,explicit models often have diculties in gen-erating large enough gaugino masses. More

specically, Komargodski and Shih proved thatrenormalizable models in which supersymme-try is broken à la O'Raifeartaigh yield vanish-ing gaugino masses at the leading order, un-less there is an instability of the supersymme-try breaking at direction in the messenger di-rection. This problem can be cured if quan-tum corrections lift the at direction in such away that the supersymmetry breaking minimum(with zero messenger vacuum expectation val-ues) becomes metastable. In collaboration withE. Dudas [t10/175], we studied under which con-ditions they can promote it to the ground stateof the theory, thus allowing for sizeable gauginomasses without metastability. We found that,in a large class of renormalizable O'Raifeartaighmodels coupled to messenger elds, the requiredcondition is the suppression (typically by a one-loop factor) of the messenger couplings to thegoldstino supereld.

B.9.2 Non-minimal supersymmetric ex-tensions of the Standard Model(M. Chemtob, S. Lavignac)

The Higgs sector of the Minimal Supersymmet-ric Standard Model suers from a ne-tuningproblem associated with the large radiative cor-rections needed to satisfy the lower bound onthe Higgs boson mass from the LEP experi-ment, mH > 114.4GeV. An elegant solutionto this problem is to realize the Higgs boson asthe pseudo-Goldstone boson of a spontaneouslybroken approximate global symmetry, so as tomaintain radiative corrections to the Higgs po-tential under control. In collaboration with A.Kaminska [t10/094], we studied a supersym-metric model in which the lightest Higgs bo-son arises as the pseudo-Goldstone boson of aglobal SU(3) symmetry. A notable dierencewith previous models is that soft terms arisefrom gauge-mediated supersymmetry breaking,which in turn provides a mechanism to breakthe global SU(3) symmetry, namely through the(calculable) tadpole of a gauge singlet eld.

In the next-to-minimal supersymmetric stan-dard model (NMSSM), the so-called µ-problemis solved by trading the bilinear Higgs bosonsterm µHuHd for the trilinear coupling HuHdSinvolving an extra singlet eld S. An economi-cal explanation of neutrino masses also becomesavailable in the generalization of the NMSSMincluding the lepton number violating trilinearcouplings LiHuS. However, the full model withthe attendant soft supersymmetry breaking cou-plings suers from the presence of scalar elddirections along which the eective potential is






unbounded from below, as well as of tachyonicmodes and charge and colour breaking minima.These instabilities impose constraints on the pa-rameters of the lepton number violating interac-tions. We have explored their implications forthe mass spectrum of the model through a de-tailed study of the mass matrices for the bosonand fermion modes in the regular electroweaksymmetry breaking vacuum [t07/113].

B.9.3 Phenomenology of string models(M. Chemtob, P. Hosteins)

Progress in the understanding of the role ofD-branes in type II superstring theories hasled (among other things) to the constructionof models with stable multiple brane setupscompatible with TeV string scale. In partic-ular, Standard Model-like solutions were builtwith four stacks of intersecting D6-branes on atoroidal orientifold. A crucial feature of thesemodels is the presence of massless fermions lo-calized at points of the internal space wherebrane pairs intersect. These open string modesinteract through tree-level exchange of massive(virtual) open string modes, leading to eec-tive local four-fermion operators. We evaluatedthe chirality-conserving contact interactions ofquarks and leptons by means of an approximatesubtraction procedure aimed at removing thestring massless and massive (KaluzaKlein) mo-mentum modes, so as to retain only the stringRegge and winding modes [t08/145]. The signa-tures of these contact interactions at high-energycolliders and in avour physics depend on twofree parameters, the string and compacticationscales. Useful constraints are derived from theircontributions to the Bhabha scattering dieren-tial cross section, to neutral meson (K0-K0, B0-B0, D0-D0) mixing and to lepton avour violat-ing three-body leptonic decays of the µ and τleptons.

Heterotic string model building has receiveda vigorous stimulus in recent years through thefocus on anisotropic type string compactica-tions, yielding eective unied gauge theoriesin ve or six spacetime dimensions with mat-ter modes distributed in the bulk or near xedbranes. Attempts to implement this scheme forthe Z6−II orbifold with two Wilson lines gaveaccess to a fertile mini-landscape of vacua real-izing extensions of the Minimal SupersymmetricStandard Model (MSSM) with decoupled exoticmodes. In [t09/154], we searched for extensionsof the MSSM with extra singlets and/or extraU(1)'s. The string theory selection rules wereused to constrain the dependence of the eective

superpotential on the various scalar eld direc-tions parameterizing the moduli space of vacua.Instead of a statistical vacuum number count-ing, we choose three representative Pati-Salamunied string models on which we performed anautomated selection of vacuum solutions satisfy-ing the D-term atness and approximate F-termatness conditions. The main purpose was toestablish an existence proof for supersymmetricvacua in which suppressed bilinear terms for theelectroweak Higgs doublets coexist with unsup-pressed trilinear couplings to suitable masslesssinglet modes.

B.10 The electroweak phase tran-sition

B.10.1 The nature of the electroweakphase transition and its cosmo-logical imprints (C. Delaunay, C.Grojean, G. Servant)

We have very limited information about the dy-namics of the electroweak phase transition in theearly Universe. It is known that it cannot be rstorder within the Standard Model, since LEPdata constrains the Higgs mass to be too largeto generate an important bump in the thermalpotential. The situation could be dierent, how-ever, if the Higgs boson self-interactions werenot the ones posited in the SM. In [t07/141], westudied the dynamics of electroweak bubble nu-cleation when the Higgs boson emerges from astrongly interacting sector as a composite boundstate.

Another interesting cosmological conse-quence of new strong dynamics at the TeV scaleis a period of supercooling in the early Universefollowed by a strong rst-order phase transition.This has barely been explored and we have inves-tigated in [t11/129] how this opens new avenuesfor addressing major cosmological puzzles suchas the genesis of dark matter and the origin ofthe matter-antimatter asymmetry. We have out-lined the very peculiar cosmological propertiescharacterizing some models of strong dynamicsat the TeV scale. In particular, we motivatedthe mechanism of cold baryogenesis in this con-text [t11/130]. A large signal in gravity wavesin the milli-hertz range would be a smoking-gunsignature of this near-conformal dynamics at theTeV scale. A gravity wave detector such as LISAwould be a completely independent window onthe electroweak scale, and could complement theinformation provided by the LHC.

In collaboration with C. Caprini, we alsoworked on analytical derivations of the spectrum








of gravitational waves due to bubble collisionsand to the induced magneto-hydrodynamicalturbulence. This work is described in the cos-mology section of this report.

B.10.2 Bubble growth in rst-orderphase transitions (J.-M. No, G. Ser-vant)

In [t10/299], we studied the hydrodynamics ofbubble growth in rst-order phase transitions.This is very relevant for electroweak baryoge-nesis, as the baryon asymmetry depends sen-sitively on the bubble wall velocity, as well asfor predicting the size of the gravity wave signalresulting from bubble collisions, which dependson both the bubble wall velocity and the plasmauid velocity. We performed this study in dier-ent bubble expansion regimes, namely deagra-tions, detonations, hybrids (steady states) andrunaway solutions (accelerating wall), withoutrelying on a specic particle physics model. Wecomputed the eciency of the vacuum energytransfer to the bubble wall and to the plasmain all regimes. We claried the condition deter-mining the runaway regime and stressed that inmost models of strong rst-order phase transi-tions this would modify the expectations for thegravity wave signal.

Following this study, we pointed out in[t10/176] that for the expansion regime of de-agrations (small, subsonic wall velocities), inaddition to the friction of the plasma on the bub-ble wall, another eect can contribute to coun-terbalancing the pressure dierence on the wallthat drives the expansion, namely the fact thatthe compression front ahead of the bubble wallfor deagrations heats up the plasma in front ofthe wall, which diminishes the pressure dier-ence on the wall. In particular, it was foundthat due to the presence of this eect, dea-grations may be achieved even for very smallor vanishing friction, contrary to usual expecta-tions. This may have important implications forelectroweak baryogenesis scenarios, for which asmall relative velocity between the wall and theplasma in front (usually assumed to be the wallvelocity) is needed, since it allows to estimatein some cases a subsonic wall velocity withoutthe need to know the precise value of the fric-tion. Finally, we showed in [t11/032] that inthe case of deagrations or hybrids, also due tothe existence of a compression front ahead ofthe bubble wall, the relative velocity betweenthe wall and the plasma in front is in generalsmaller than the wall velocity, and this eect islarger for stronger phase transitions. Therefore

it may be possible to have a small relative ve-locity between the wall and the plasma in frontwhile the bubble expands with a relatively largevelocity, opening the possibility of sizable grav-itational wave background signals in scenarioswhere electroweak baryogenesis is possible.

B.11 Dark matter

B.11.1 Dark matter phenomenology andmodel-building (M. Cirelli, F. Iocco,P. Panci, G. Servant)

Dark matter constitutes most of the matter con-tent of the Universe, as a number of cosmologi-cal and astrophysical observations now conrm.However, little is known about its nature andit has not been directly detected yet. There aremany new particle candidates that might consti-tute dark matter, coming from dierent theoriesbeyond the Standard Model, and this has beenan incredibly rich and varied area of research inthe last twenty years.

Until a few years ago, most studies concen-trated on supersymmetric candidates. However,in the last decade, a plethora of new candi-dates have been studied as it has been real-ized that most standard Model extensions at-tempting to solve the hierarchy problem containweakly-interacting dark matter candidates intheir spectrum. Non-supersymmetric dark mat-ter candidates have been reviewed in [t10/303],emphasizing the connection with new physics atthe electroweak scale, in particular in the con-text of new constructions suggested in the lastdecade, such as Little Higgs or composite Higgsmodels.

We continued the investigation of MinimalDark Matter, a new model proposed a few yearsago by us. In contrast with the usual, more elab-orated approaches to dark matter pursued in thecontext of theories beyond the Standard Model,an extra matter multiplet is simply added on topof the Standard Model. We found that a properassignment of the gauge quantum numbers auto-matically ensures that one of these candidates isstable (the fermionic quintuplet with zero hyper-charge). This theory is so simple that it allowsto fully compute the dark matter phenomenol-ogy (interactions with nucleons in undergroundexperiments, annihilation products, etc.), lead-ing to precise predictions for the next generationof dark matter experiments. The study of thisphenomenology has been the topic of [t07/052],which focuses on the relic abundance productionin the early Universe (and, in passing, describesthe formalism for the so-called Sommerfeld en-






hancement that became later of wide interest inthe community) and of [t08/034], which focuseson predicting the uxes of positrons, antiprotonsand gamma rays from the annihilations of Min-imal Dark Matter particles in the galactic halo.Our work on Minimal Dark Matter has been col-lected in an invited review [t09/010].

In the framework of more general analysesof dark matter phenomenology, we analysed in[t09/027] (in collaboration with C. Bräuninger,a master student) another interesting possiblesignal of dark matter indirect detection: uxesof anti-deuterium synthetized in galactic annihi-lations. The study focussed on the very heavyDark Matter scenarios individuated by the re-cent data, and found promising perspectives es-pecially for primary annihilation channels intoquarks. In [t09/082], we also studied the im-plications of dark matter annihilations on starevolution. We investigated the possible observ-able modications to the characteristic lifetimeof early stars in case they are powered by darkmatter annihilations, and found that the eectswould be detectable only for extreme regimes.

With a number of international collabora-tors, we embarked in 2010 on a systematic,model-indepedent compilation of results usefulfor indirect dark matter detection, both in termsof formulae and in terms of numerical func-tions/tables that can be adapted to compute vir-tually any dark matter signature. The resultshave led to [t10/025], a publication that hope-fully will prove useful for many researchers inthe community.

B.11.2 Dark matter and Grand Unica-tion (M. Frigerio)

The cosmological and astrophysical evidence fordark matter can be accounted for by a new,stable particle with the appropriate annihila-tion cross section, typically a weakly interact-ing particle with a mass in the TeV range. Itturns out that the addition of such a state tothe Standard Model makes it possible for gaugecouplings to unify without low-energy supersym-metry. The dark matter particle should be afermion isotriplet with zero hypercharge, T ≡(T+, T 0, T−), that could be seen in future directdetection experiments. In collaboration with T.Hambye, we showed in [t09/285] that this can-didate is uniquely selected if we require that i)its stability is ensured by the grand unied sym-metry, and ii) the addition of this state to theStandard Model leads to gauge coupling uni-cation above the scale corresponding to the ex-perimental lower bound on the proton lifetime,

MGUT > 1015 GeV.

B.11.3 Extra-dimensional dark matter(G. Servant)

For a Weakly Interacting Massive Particle(WIMP) to be a viable dark matter candidate,it should be stable. In supersymmetry, this oc-curs because of a new discrete symmetry: R-parity. In Little Higgs models, the underlyingsymmetry is a the so-called T-parity. In extra-dimensional models, this is KaluzaKlein (KK)parity. However, KK parity is a good symmetryonly in specic extra-dimensional models, thosewith at extra dimensions. On the other hand,most of the interesting phenomenology (as far asaddressing the hierarchy problem is concerned)arises in the context of warped extra dimen-sions (RandallSundrum models). In this con-text, KK parity is broken by the Anti-de-Sittergeometry and there is no stable KaluzaKleinstate. In [t07/153], we made the rst attemptto implement a KaluzaKlein parity in warpedcompactications by gluing two identical slicesof 5D AdS in either the UV or the IR region.Model-building issues as well as phenomenologi-cal properties were discussed. Collider signals ofthe warped KK parity are dierent from eitherthe conventional warped extra dimension with-out KK parity, in which the new particles are notnecessarily pair produced, or the KK parity inat universal extra dimensions, where each KKlevel is nearly degenerate in mass. Dark mat-ter and collider properties of a TeV mass KK Zgauge boson as the Lightest KaluzaKlein parti-cle were discussed. Phenomenology at the LHCof extra-dimensional dark matter was reviewedin the book chapter [t10/058].

B.11.4 A top quark - dark matter con-nection (G. Servant)

In [t09/315], we explored the possibility that thetop quark has important couplings to dark mat-ter. If the dark matter particle arises as part ofthe dynamics of electroweak symmetry break-ing, it is natural to expect it to have large cou-plings to the most massive states of the Stan-dard Model, in particular to the top quark, andsuppressed couplings to the light SM degrees offreedom. If this is the case, dark matter willcouple at the loop level both to photons andto the Higgs boson, and the Higgs boson couldbe copiously produced in the galaxy in associ-ation with a photon from dark matter annihi-lations or decays. The resulting photon spec-trum possesses a line whose energy reects themass of the Higgs and of the WIMP and does











not arise if dark matter is a scalar or a Majo-rana fermion, thus providing information aboutthe WIMP spin and statistics. Indirect detec-tion of WIMPs annihilating or decaying in ourgalaxy into high energy gamma rays could po-tentially be our rst indication that WIMPs areelectroweakly active particles, and our rst non-gravitational glimpse of dark matter thanks totelescopes such as FERMI. This implies that theFermi/GLAST satellite and ground-based AirCherenkov telescopes could probe the Higgs bo-son and complement information obtained at theLHC. We have illustrated this phenomenon in acase in which the WIMP is composed of Diracfermions annihilating via a massive vector res-onance (Z ′) which couples strongly to the topquark, serving as a portal between dark matterand the Standard Model. Our setup arises nat-urally in models in which the top quark acquiresits mass through a large mixing with compositestates in a new strongly interacting sector.

B.11.5 Dark matter interpretation ofcosmic ray data (M. Cirelli, F.Iocco, P. Panci, G. Zaharijas)

During the summer of 2008, the PAMELA satel-lite announced preliminary data on the positronux in cosmic rays, showing conrmation of anexcess over the expected background that pre-vious experiments had already exposed. Soonafter, we compared in [t08/163] the uxes fromMinimal Dark Matter annihilations predicted in[t08/034] with these data. We found a remark-ably good agreement and were able to determinethe set of astrophysical parameters giving thebest t. Then we started a model-independentinterpretation of the data in charged cosmicrays (positrons, but also antiprotons from thePAMELA satellite, and electrons + positronsfrom ATIC, FERMI, HESS and other experi-ments), with the goal of identifying the darkmatter models that are capable of explainingthe observed signals while remaining compat-ible with searches in all other channels. Wefound that the PAMELA results alone, if dueto dark matter annihilations, individuate quiteunusual dark matter properties: either a veryheavy particle (above 10TeV) or a lighter oneannihilating mainly into leptonic channels suchas e+e−. Adding the balloon datasets in theanalysis leaves us with the second possibilityonly [t08/139].

No claim of a dark matter signal in cos-mic ray data can be supported without a crit-ical inspection of the associated eects that itshould entail. This led us to investigate the

constraints on the dark matter interpretationsdiscussed above, coming from: i) gamma raysand synchrotron radiation from the galactic cen-ter and from dwarf satellite galaxies [t08/184];ii) the ux of gamma rays produced by inverseCompton scattering of energetic positrons on thelow-energy ambient photons in the galactic halo[t09/030], [t09/187] (a signal that has the ad-vantage of being less sensitive to astrophysicaldetails than the gamma rays from the galacticcenter); iii) the ux of isotropic, and thereforeextragalactic, gamma rays [t10/229]; iv) the cos-mological evolution of the Universe [t09/046],[t09/065], based on the fact that dark matterannihilations during the epoch of galaxy forma-tion would inject charged particles and energy,producing reionization and heating of the pri-mordial gas which can exceed current measure-ments of the optical depth of the Universe, andmodifying the spectra of the Cosmic MicrowaveBackground (CMB). The bottom line of all theseanalyses is that the lack of associated signals im-pose very stringent constraints on the dark mat-ter interpretations of charged cosmic ray data, aresult which is now agreed upon by most of thecommunity.

In [t10/229], [t10/230], the FERMI collab-oration has looked at possible anisotropies inthe arrival direction of leptons (electrons andpositrons) which could betray their origin froma local astrophysical source (as opposed to asmoothly distributed dark matter): bounds arefound and some bright sources can be excluded.G. Zaharijas, a member of the FERMI collabo-ration, is the corresponding author for [t10/229].These works have been presented at a large num-ber of meetings, often in the form of more gen-eral reviews on the status of dark matter indirectdetection, as in [t09/178], [t10/098].

In [t10/062], we examined a class of darkmatter models often advertised as being able toexplain the cosmic ray excesses, namely mod-els with multistate dark matter coupled to lighthidden sector bosons. A detailed calculationshowed that these models actually suer fromseveral tensions with the gamma ray constraintsand in reproducing the cosmological abundanceof dark matter. They can therefore only verymarginally be considered viable.

B.11.6 Neutrino cosmology (M. Cirelli)

Neutrinos have an important impact on cosmol-ogy at various stages, most notably because theirstreaming on cosmological distances in the earlyUniverse helped shaping the distribution of thegalactic structures that we observe today. Re-

















cent experiments and satellites have made it pos-sible to observe such eects with increasinglygood precision, making it possible to constrainboth the sum of neutrino masses and the totalnumber of neutrinos (the latter is meant to in-clude the three neutrinos of the Standard Model,plus any exotic light weakly interacting particlethat behaves like a neutrino). We worked onseveral of these aspects in the past and closelyfollow the recent developments. We presentedseveral reviews on this topic [t08/200], [t10/167].

B.12 Particle physics models forthe early Universe

B.12.1 Ination (P. Brax, E. Cluzel, S.Mariadassou)

In the last four years, we have studied a certainnumber of inationary models and their con-sequences for preheating and the formation ofcosmic strings. We investigated the KKLT sce-nario of supersymmetry breaking [t07/176] andits coupling to ination. In particular, we haverealised the rst fully gauge invariant setting ac-commodating both KKLT stabilisation of themoduli and ination [t07/178]. In these gen-eralised racetrack models, a generic predictionis that the spectral index is low like in smalleld ination [t07/180]. We have also stud-ied the possible formation of cosmic strings atthe end of ination in these scenarios [t08/227],[t08/228]. Cosmic strings may also result fromthe presence of extra U(1)'s in models extend-ing the usual Abelian Higgs model to non-linearactions of the DBI type [t08/155]. The pre-heating phase of inationary models is crucialand may lead to the non-perturbative creationof gravity waves and black holes. With Jean-Francois Dufaux, we have considered preheat-ing for small eld ination [t10/205]. We havefound that tachyonic and resonance preheatingsare both crucial. Although not detectable withfuture experiments, gravity waves are also co-piously produced. Finally, we have studied thecreation of particles when two branes cross eachother in DBI ination [t09/265]. This leads toan abrupt jump in the power spectrum of pri-mordial uctuations like in Starobinsky's modelfor Cosmic Microwave Background (CMB) fea-tures [t11/112].

B.12.2 Supersymmetry breaking and in-ation (P. Brax, C. Savoy, A. Sil)

A remarkable property of a class of asymptot-ically free supersymmetric QCD-like theories isduality: in the strongly-coupled regime they aredescribed by the metastable potential of a dual

supersymmetric theory. This has recently beenput forward by Intriligator, Seiberg and Shih asa natural framework for supersymmetry break-ing. We suggested a somewhat analogous de-scription for the sector responsible for (hybrid)ination, such that the reheating temperatureand the measured ination parameters are re-lated to the gauge coupling and mass parame-ter of a supersymmetric QCD theory. We iden-tied the R-symmetries of the inationary andsupersymmetry breaking sectors, assumed to bedescribed by two independent supersymmetricQCD theories that are only coupled through su-pergravity. Then, xing the ination parame-ters from CMB data, we derived the supersym-metry breaking scale and obtained a rationalefor the Universe to be stuck in the metastablesupersymmetry breaking vacuum after ination[t07/117], [t08/230], [t09/213].

B.12.3 Dark energy and modied gra-vity (P. Brax)

In 2007, we started studying the possible obser-vation of scalar eld models coupled to matterin laboratory experiments [t07/092]. We havefocussed on three types of experiments whereour work prompted a large body of experimentalwork. In particular, we have analysed the optical[t07/175] and Casimir consequences [t07/177] ofchameleon models which may lead to the ac-celeration of the Universe while being screenedin gravitational tests of fth forces and equiva-lence principle violation. In optics, chameleonsmay be produced via the Primako eect ina magnetic eld. This may happen in opti-cal cavities and is being looked for by experi-ments such as CHASE at Fermilab or BMV inToulouse. Scalar elds may induce a new forcein Casimir experiments. In particular, this forcecould be screened when the material in betweenthe Casimir plates in dense enough while presentin vacuum. We have been awarded a grant tocarry out this experiment in Amsterdam underthe supervision of D. Iannuzzi [t10/215]. Finally,the CAST experiment may see back-convertedX-ray photons from chameleons created in thesolar tachocline [t10/214]. This project will beone of the CAST objectives starting from 2011.Other possibilities such as atomic precision tests[t10/206] and afterglow experiments [t10/209]have been envisaged. We also applied the Eot-wash constraints to f(R) models and deducedstrong constraints on the equation of state ofdark energy [t08/229].

We have also studied chameleons with elddependent couplings [t10/211]. Using path inte-
























gral methods, we have calculated the coupling ofscalar elds to photons in scalar-tensor theories[t10/207]. We have studied shift symmetric darkenergy models in supergravity [t09/211] and thecoupling of ination to dark energy [t08/235].

We have thoroughly studied the coupling ofdark energy to the Standard Model and theconsequences for accelerator physics. We haveshown that the coupling to the Higgs sector issensitive to high energies and to the UV com-pletion of both the Higgs and the dark energysectors. This implies that the creation of Higgsparticles via WW fusion may be inuenced bythe presence of a dark energy sector [t09/212],[t09/209].

We have studied a possible application of theAdS/CFT setup in a cosmological context andlinked the acceleration of the Universe with theconformal anomaly in this case [t10/210].

Following our original work in 2002 and2004, we have studied the modication of thegrowth of structures induced by the presence ofa cosmologically coupled scalar eld (such as achameleon) [t10/105]. We have considered thelinear regime [t10/205], the second order per-turbation theory and the bispectrum [t11/099],and nally the non-linear stages both analyti-cally with the spherical collapse model [t10/213]and numerically with large N-body simulations[t11/113]. These eorts are particularly worth-while for dilatonic models [t10/212] where localtests of gravity imply that modied gravity oc-curs on galaxy cluster scales. We are extend-ing our work to galileon models and also toCMB precision tests which will be soon avail-able thanks to the Planck satellite.

Finally, we have given lectures on dark en-ergy [t09/264].

B.13 Gauge theory amplitudes

B.13.1 Symmetries of scattering ampli-tudes in gauge theories (G. Ko-rchemsky)

Gauge theories have been and will remain thecorner stone of all models unifying the ele-mentary particles. The Large Hadron Collider(LHC) experiment will probably provide evi-dence for new physics at the multi-TeV energyfrontier. In order to exploit fully the poten-tial of the LHC, new approaches to the study ofmultiparticle scattering processes in the under-lying gauge theories need to be developed. Thisis of crucial importance for the ecient evalu-ation of the signicant background of StandardModel physics, against which the signals for new

physics have to be assessed.Until recently, the standard approach to

computing scattering processes in gauge theo-ries relied on a perturbative Feynman diagramexpansion. While this procedure is very wellunderstood, the complexity of the calculationgrows so rapidly with increasing the number ofparticles that it seriously challenges our ability,especially beyond the leading order, to computebackground processes to the accuracy requiredby the LHC physics. This calls for developinga new technique for computing various observ-ables in gauge theories.

In the past few years several remarkable de-velopments took place. They concern a specialtype of gauge theory, the maximally supersym-metric N = 4 Yang-Mills theory (N = 4 SYM),the rst example of an ultraviolet nite quan-tum eld theory. As a consequence, it exhibitsconformal symmetry at the quantum level avery unusual feature for four-dimensional quan-tum eld theory. Although the N = 4 SYMLagrangian diers from that of QCD, the twogauge theories share many common features andprogress in understanding the properties and indeveloping new calculation methods for N = 4SYM can have direct relevance for QCD andfor the Standard Model. For example, tree-levelgluon amplitudes are the same in all gauge theo-ries, and thus new results for N = 4 SYM can beimmediately applied to the calculation of multi-jet event background at LHC.

Dual superconformal symmetry

The scattering amplitudes in maximally super-symmetric N = 4 SYM theory have a numberof remarkable properties both at weak and atstrong coupling. Dened as matrix elements ofthe S-matrix between asymptotic on-shell states,they inherit the symmetries of the underlyinggauge theory. In addition, trying to understandthe properties of the scattering amplitudes, onecan discover new dynamical symmetries of theN = 4 theory. In a series of papers, we ar-gued that the planar scattering amplitudes inN = 4 SYM theory have a hidden symmetrythat we called the dual superconformal symme-try. It appears on top of all well-known sym-metries of the scattering amplitudes (supersym-metry, conformal symmetry, etc.) and is not re-lated (not in an obvious way, at least) to an in-variance of the Lagrangian of the theory (see[t09/076, t09/102, t10/013]). At strong cou-pling, the same symmetry also emerges in theAdS/CFT description of scattering amplitudes,from invariance of the string sigma model on an


















AdS5×S5 background under a combined bosonicand fermionic T-duality. It is even more intrigu-ing that the dual conformal symmetry is alsopresent in QCD but only in the Regge limit (see[t09/284]). It worth mentioning that it is in thislimit that QCD is believed to admit a dual de-scription in terms of a (still mysterious) hadronicstring. In close analogy with N = 4 SYM, weexpect that dual conformal symmetry providesyet another glimpse into the QCD/string dual-ity.

Scattering amplitudes / Wilson loops /Corrrelation function duality

Based on the previous QCD ndings and onstrong coupling analysis of scattering amplitudeswithin AdS/CFT correspondence by Alday-Maldacena, we have previously demonstratedthat MHV scattering amplitudes in planar N =4 theory are related to Wilson loops evalu-ated on closed polygon-like contours in a dualMinkowski space-time, consisting of light-likesegments dened by the on-shell gluon mo-menta.

We have argued in [t10/091, t10/092,t10/139] that the duality between MHV am-plitudes and light-like Wilson loops can be ex-tended to include the duality to the correla-tion functions of conformal primary operatorslocated at the vertices of the same polygon-like contour. One of the consequences of thisrelation is that the dual conformal symmetryof the MHV amplitudes can be derived fromthe conventional conformal symmetry of thelight-like Wilson loops and the correlation func-tions. To verify the duality, we studied in[t10/091, t10/092, t10/139] the correlation func-tions of half-BPS protected operators in N = 4super-Yang-Mills theory in the limit where thepositions of the adjacent operators become light-like separated. We computed the loop correc-tions by means of Lagrangian insertions andshowed, in a number of examples at one andtwo loops, that the logarithm of the correlationfunction coincides with twice the logarithm ofthe matching MHV gluon scattering amplitude.

In a recent development (see [t11/034,t11/036, t11/037]), we further extended the du-ality between MHV amplitudes and the light-cone limit of correlation functions to genericnon-MHV amplitudes in planar N = 4 SYMtheory. We considered the natural general-ization of the bosonic correlation functions tosuper-correlators of stress-tensor multiplets andshowed, in a number of examples, that theirlight-cone limit exactly reproduces the square of

the matching super-amplitudes. We found thatthe super-correlators computed at Born level canbe eectively used to compute various scatteringamplitudes in planar N = 4 SYM theory: If allpoints of the super-correlator form a light-likepolygon, the correlator is dual to the tree-levelamplitude. If a subset of points are not on thepolygon but are integrated over, they becomeLagrangian insertions generating the loop cor-rections to the correlator. In this case the du-ality with amplitudes holds at the level of theintegrand. We build up the superspace formal-ism needed to formulate the duality and presentthe explicit example of the NMHV tree ampli-tude as the dual of the lowest nilpotent level inthe correlator.

Cusp anomalous dimension

The cusp anomalous dimension is a ubiquitousquantity in N = 4 Yang-Mills theory, and itis one of the best investigated observables inthe AdS/CFT correspondence. In application tothe scattering amplitudes, the cusp anomalousdimension controls the structure of leading in-frared singularities. In planar N = 4 SYM the-ory, perturbative expansion of the cusp anoma-lous dimension at weak coupling has a nite ra-dius of convergence while at strong coupling itadmits an expansion in inverse powers of the 'tHooft coupling which is given by a non-Borelsummable asymptotic series. In [t08/220], westudied the cusp anomalous dimension in thetransition regime from strong to weak coupling.We argued that the transition is driven by non-perturbative, exponentially suppressed correc-tions. To compute these corrections, we revis-ited the calculation of the cusp anomalous di-mension in planar N = 4 SYM theory and ex-tended the previous analysis by taking into ac-count nonperturbative eects. We demonstratedthat the scale parameterizing nonperturbativecorrections coincides with the mass gap of thetwo-dimensional bosonic O(6) sigma model em-bedded into the AdS5×S5 string theory. This re-sult is in perfect agreement with the predictioncoming from the string theory consideration.

B.13.2 New techniques for scatteringamplitudes (R. Britto, E. Mirabella)

On-shell techniques for one-loop ampli-tudes

We have been nding and developing new tech-niques for computing scattering amplitudes inQCD, especially in processes with many nalstates, and through next-to-leading-order in thecoupling constant. These new techniques, in













which all intermediate quantities are on-shelland gauge invariant, are ecient and yield ex-pressions for amplitudes in their most compactforms. Our methods, summarized in [t10/257],have been used to obtain certain gluon ampli-tudes for the rst time, at tree level and one-loop order. Each of these computations repre-sents an improvement in general methodologythat can be applied to broad classes of ampli-tudes. One strength of this approach, comparedwith more traditional methods, is that it ap-plies to amplitudes with an arbitrary numberof particles. By any technique, but especiallytraditional ones, the complexity of a computa-tion increases rapidly with the number of exter-nal particles. The reason that my approach cangeneralize is that it is mainly independent of thefeatures of individual integrals.

This research follows two principal lines.First, we have been developing these techniquesfor one-loop amplitudes with a view towards e-cient, automatic, algorithmic computation. Theframework of these calculations overlaps a greatdeal with that of D. Kosower. Our particularspecialty is in deriving compact analytic expres-sions. Therefore, we have been working withsymbolic computation (Mathematica) to imple-ment these techniques and learn how to get thebest results as eciently as possible. At thesame time, we aim to develop a numerical coun-terpart to this analytic algorithm and measureits eciency against other methods.

Extensions to more general amplitudes

Second, we have been widening the realm ofapplicability of the techniques for calculatingloop amplitudes. They are fully developed forone-loop amplitudes where all the virtual par-ticles are massless, which is sucient for mostQCD background processes at the LHC. How-ever, in a general theory where the virtual par-ticles might have signicant masses, one-loopamplitudes have additional components whichare much more dicult to determine by on-shellmethods. One of these additional componentsare the so-called tadpole integral contributions.The on-shell approach to one-loop amplitudesis to use unitarity cuts, which are operationsrestricting certain chosen propagators to theirmass shells, combined with knowledge of a com-plete set of master integrals which are knownexplicitly and form a linear basis for any Feyn-man integral. If at least two propagators are cutin this fashion, the result is a singularity of theamplitude associated with a certain momentumchannel. If only one propagator is cut, there

is no physical momentum channel to serve asa point of reference. This is the problem withthe tadpole integral contributions, which arethe integrals with only one propagator remain-ing in the denominator. We have outlined twoproposals for computing these tadpole contribu-tions. First, in a joint publication with B. Feng[t09/332], we found that it is possible to addone more (unphysical) propagator in a formalsense, cut it along with the existing propagator,use our previous methods for traditional cuts,and nally decouple the eects of the unphysicalpropagator. Second, in a joint publication withE. Mirabella [t10/254], we studied the meaningof the single-cut integral in itself. Not only doesit lack a simple interpretation in terms of ex-ternal kinematics, but moreover it typically di-verges and picks up contributions from functionsother than the master integrals. Nevertheless,we found that divergences could be regularized,and that with a careful, though dicult treat-ment, not only can tadpole contributions be de-termined, but in principle every other kind ofcontribution can be identied uniquely as wellin this cut. We are continuing to study the im-plementation of single cuts in physical scatteringprocesses.

B.13.3 NLO amplitudes (D. Kosower)

BlackHat software library

The primary activity in NLO QCD was withinthe BlackHat collaboration, developing and ap-plying the BlackHat software library. This li-brary uses on-shell methods unitarity and on-shell recursion to compute one-loop amplitudesnumerically. The basic idea behind on-shellmethods is to use only information about phys-ical states in calculations of amplitudes, and toturn general properties factorization, unitar-ity, and the existence of a representation basedon Feynman integrals into tools for perform-ing calculations. These on-shell methods haveprovided a means of breaking the long-standingbottleneck to NLO calculations of processes withseveral jets in the nal state, that of computinghigher-multiplicity one-loop amplitudes in QCD.The basic ideas and approach to a numerical im-plementation of the on-shell methods were re-ported in [t08/054]. Calculations of several one-loop amplitudes were reported in various con-ference proceedings [t08/117, t08/123]. Severalphysics applications followed: the computationof the NLO cross section for W+3-jet produc-tion at both the Tevatron and the LHC, re-ported in refs. [t09/019, t09/078, t09/136]; theNLO prediction for Z, γ∗+3-jet cross sections at











the Tevatron [t10/040, t10/065, t09/268]; anda landmark result, the NLO prediction for theproduction of W+4-jet production at the LHC[t10/111]. The W+4-jet process is an impor-tant background to top-pair production as wellas the discovery of new physics beyond the Stan-dard Model. We have also pointed out the typi-cal left-handed polarization of bothW± at largetransverse momentum, an eect distinct fromthe well-known polarization at small transversemomentum, and one that should be useful indistinguishing `prompt'W s from those arising indecays of heavy states [t09/268, t11/040]. Otherrelated work by S. Badger included a new tech-nique for computing rational terms in QCD am-plitudes [t08/106] and its application to an un-expected simplicity in QED and gravity ampli-tudes [t08/156].

N = 4 maximally supersymmetric YangMills theory

Calculations in the N = 4 maximally super-symmetric YangMills theory are important as asimple laboratory for developing techniques forQCD, and also important in their own right fordeepening our understanding of the AdS/CFTduality between strings (strong coupling) andthis gauge theory (weak coupling). With a va-riety of collaborators, I computed two two-loopsix-point amplitudes in the N = 4 theory, theMHV [t08/045] and NMHV ones [t08/045]. Theformer was crucial in establishing the connec-tion with a Wilson-loop calculation, and in con-rming the existence of a `remainder' functionbeyond the simple exponentiation hypothesis ofBern, Dixon and Smirnov. The latter furnishesadditional such functions, targets for any at-tempt to link weak and strong coupling. Otherwork in this area, by H. Johansson and collabo-rators, included the computation of the completefour-loop amplitude, including non-planar terms[t10/075]; the observation that a novel structurefor the kinematic terms paralleling color coe-cients in gauge theories, extends to loop ampli-tudes, thereby extending the notion of gravityamplitudes as a `double copy' of gauge-theoryamplitudes and hinting at new structures un-derlying the latter [t10/044, t10/086]; and a re-view of unitarity and other modern techniquesfor higher-loop amplitudes [t11/029].

New approach to parton showers

A third subject is that of developing a new ap-proach to parton showers, based on the use of2 → 3 branching antennæ instead of the usual1 → 2 collinear splitting functions. This allows

one to preserve masslessness at all stages of theshower [t07/107]; oers an understanding of theeect of nite terms neglected in previous ap-proaches [t07/107]; and opens the way to newapproaches to matching to nite-order matrixelements [t10/196].

B.13.4 SUSY particle production (E.Mirabella)

Pair production of squark and gluino is the mostimportant discovery channel of TeV-scale super-symmetry at the LHC. An extremely interest-ing and challenging ongoing project is the com-putation the electroweak contributions to theseprocesses. These contributions, together withthe known QCD corrections, complete the NLOanalysis.

Electroweak corrections include O(αsα),O(α2) and O(α2

sα) contributions. The latter arethe more involved ones, e.g. they include thefull set of one-loop QCD graphs interfering withthe tree-level electroweak diagrams. In order toobtain UV nite results, the MSSM has to becompletely renormalized at next-to-leading or-der, properly taking care of dierent regulariza-tion schemes in the presence of supersymmetry.The soft and collinear divergences are cancelledby real photon and real gluon emission. Owingto their complexity, we regularized and isolatedthese divergences using both phase space slic-ing and dipole subtraction methods, with massregularization as well as dimensional regulariza-tion. The impact of the electroweak contribu-tions on the total cross section is at the levelof several percent and can be even more sig-nicant in the kinematical distributions. Thelatest results on this project concern squarksquark [t10/007] and sbottomanti-sbottom pairproduction [t11/021].

We have computed the NLO electroweakcontributions to the semi-inclusive bottom-Higgsproduction [t10/284]. This process is an impor-tant discovery channel for supersymmetric Higgsboson for large values of tanβ.

B.14 Jet algorithms (G. Soyez)Jets seen in a rst approximation as a proxyfor the hard partons produced in hadronic colli-sions are common objects, present in a largenumber of analyses and understanding thembetter has therefore the potential of translat-ing immediately into improved analyses e.g. fornew-physics searches.

B.14.1 Optimal jet radius

In order to compare the behavior of dierent jetdenitions, we had done a Monte-Carlo study of






















the mass reconstruction of a resonance decayinginto two jets, showing that optimizing the radiusused in the jet reconstruction could lead to a sig-nicant improvement. In this work, it has beenshown that the results of these simulations canbe understood analytically. This is one of thefew analytic results constraining the parametersof the jet denitions.

B.14.2 Jets in heavy ion collisions

The study of jets in heavy-ion collisions, wherethe contribution from the Underlying Event i.e. the soft background produced together withthe hard probes spoils their ecient recon-struction, the reconstruction of jets is particu-larly challenging. Developing around the ideathat the background contribution can be sub-tracted using jet-area-based methods, we havemade in [t10/298] an extensive study of dierentreconstruction scenarios showing that a decentresolution is achievable and suggesting varioustechniques to improve it further.

Still in the context of heavy-ion collisions,we have addressed concerns in [t11/126] aboutthe recent measurements of the dijet asymme-try at the LHC. While this observable is cer-tainly aected by in-medium quenching eects,the (intra-event) uctuations of the soft back-ground also aects the dijet asymmetry. Thismeans that a quantitative statement about thenature of quenching eects is hard to make with-out further constraints on the background uc-tuations.

Finally, we have performed in [t11/125] acomputation of the ratio between the inclusivejet cross-section computed with the same algo-rithm but 2 dierent radii at NLO in perturba-tive QCD, and shown that this observable canhave rather large non-perturbative correctionsthat could also be estimated analytically. Thisobservable can be measured at RHIC (both inpp and AuAu collisions) as well as at the LHC.

B.14.3 FastJet package

The FastJet package (see www.fastjet.fr) a package that implements a series of jet-clustering algorithms and related tools such asjet areas has now become the common inter-face to jet clustering: it is used both by the LHCexperiments in their respective analysis soft-wares and by the theorists studying jet physics.This has triggered many discussions, in particu-lar with the LHC experimentalists, even more sosince the anti-kt algorithm, that we have intro-duced in 2008, has been adopted as the defaultjet-clustering algorithm at the LHC. As a con-

sequence, new features are regularly added: wehave released FastJet v2.4.2 in February 2010,v2.4.3 in April 2011, and v3.0 shall be availablesoon.

B.15 Color Glass Condensate

At high energy, a hadron or nucleus becomes adense system of weakly-coupled gluons. How-ever, the weakness of the coupling `constant' iscompensated by the large gluon density, lead-ing to an important non-linear eect known asgluon saturation. The theoretical study of sucha system requires resummations of the naiveperturbation theory, which are best handled byan eective theory based on QCD known asthe Color Glass Condensate (CGC). The gen-eral ideas of this approach are conrmed, atleast qualitatively, by the existing experimentaldata in electron-proton collisions and in nucleus-nucleus collisions. We have written recently areview on the subject [t10/066].

B.15.1 Angular ordering in the evolutiontowards saturation (E. Iancu)

Another eect which is neglected by the stan-dard evolution equation for the CGC, the`JIMWLK equation', but which may be impor-tant for the distribution of particles in the -nal state, is the angular ordering of the suc-cessive gluon emissions, related to quantum co-herence in the process of radiation. This or-dering is correctly accounted for by the lin-ear CCFM equation, which however misses thenon-linear physics of gluon saturation. In Refs.[t09/173, t09/174] we provided a heuristic gener-alization of the CCFM equation which includessaturation via an absorptive boundary condi-tion. We have also considered the eects of arunning coupling and performed detailed numer-ical studies of the evolution of the gluon distri-bution, as described by this new equation.

B.15.2 BFKL physics in hadron-hadroncollisions (C. Marquet)

A model was developed to describe diractiveevents in hadron-hadron collisions where a ra-pidity gap is surrounded by two jets [t09/095].The hard color-singlet object exchanged in thet-channel and responsible for the rapidity gap isdescribed by the pQCD Balitsky-Fadin-Kuraev-Lipatov Pomeron, including corrections due tonext-to-leading logarithms. The model is ableto reproduce all Tevatron data, and allows to es-timate the jet-gap-jet cross section at the LHC.









B.15.3 Geometric scaling (E. Iancu, R.Peschanski)

Geometric scaling in Mueller-Navelet jets

The CGC approach is well suited for the calcu-lation of observables involving large separationsin rapidity, like forward jets. In particular, wehave predicted that the Mueller-Navelet jets apair of forward-backward jets should be sen-sitive to gluon saturation at the LHC energiesand in particular exhibit the phenomenon of ge-ometric scaling [t08/084], originally observed indeep inelastic scattering at HERA. The Mueller-Navelet jets are about to be measured at theLHC, so our prediction should be soon con-fronted with the data.

Scaling in HERA data

In [t08/062], using the Quality Factor (QF)method, we analyze the scaling properties ofdeep-inelastic processes at HERA and xed tar-get experiments for x<0.01. We look for scalingformulae of the form σ(τ), where τ(logQ2, Y ) isa scaling variable suggested by the asymptoticproperties of QCD evolution equations with ra-pidity Y . We consider four cases: Fixed Cou-pling, corresponding to the original geometricscaling proposal and motivated by the asymp-totic properties of the Balitsky-Kovchegov (BK)equation with xed QCD coupling constant, twoversions Running Coupling I,II of the scal-ing suggested by the BK equation with run-ning coupling, and Diusive Scaling suggestedby the QCD evolution equation with Pomeronloops. The Quality Factors, quantifying thephenomenological validity of the candidate scal-ing variables, are tted on the total and DVCScross-section data from HERA and predictionsare made for the elastic vector-meson and forthe diractive cross-sections at xed small xpomor β. The rst three scaling formulae have com-parably good QF while the fourth one is disfa-vored. Adjusting initial conditions gives a sig-nicant improvement of the Running CouplingII scaling.

QCD Traveling Waves

In [t09/298], we identify the nonlinear evolu-tion equation in impact-parameter space for theSupercritical Pomeron in Reggeon Field The-ory as a 2-dimensional stochastic Fisher andKolmogorov-Petrovski-Piscounov equation. Itexactly preserves unitarity and leads in its ra-dial form to an high energy traveling wave solu-tion corresponding to an universal" behavior ofthe impact-parameter front prole of the elasticamplitude; Its rapidity dependence and form de-

pend only on one parameter, the noise strength,independently of the initial conditions and ofthe non-linear terms restoring unitarity. The-oretical predictions are presented for the threetypical dierent regimes corresponding to zero,weak and strong noise, respectively. They havephenomenological implications for total and dif-ferential hadronic cross-sections at colliders.

In [t09/302], we dene a mapping of theQCD Balitsky-Kovchegov equation in the dif-fusive approximation with noise and a general-ized coupling allowing a common treatment ofthe xed and running QCD couplings. It corre-sponds to the extension of the stochastic Fisherand Kolmogorov-Petrovski-Piscounov equationto the radial wave propagation in a mediumwith negative-gradient absorption responsiblefor anomalous diusion, noninteger dimension,and damped noise uctuations.

In the paper [t08/060], using the relationof a set of nonlinear Langevin equations withreaction-diusion processes, we note the exis-tence of a maximal strength of the noise forthe stochastic traveling wave solutions of theseequations. Its determination is obtained us-ing the eld-theoretical analysis of branching-annihilation random walks near the directed per-colation transition. We study its consequencefor the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation. For the related Langevinequation modeling the Quantum Chromody-namic nonlinear evolution of the gluon densitywith rapidity, the physical maximal-noise limitmay appear before the directed percolation tran-sition, due to a shift in the traveling-wave speed.In this regime, an exact solution is known froma coalescence process. Universality and otheropen problems and applications are discussed inthe outlook.

B.15.4 Global ts to HERA data (J. Al-bacete)

In [t10/197], we demonstrated that the run-ning coupling BK equation provides a very gooddescription of the inclusive structure functionsin electron-proton collisions at small-x fromHERA, including the latest high precision datafrom the combined analysis from the H1 andZEUS collaborations. We also showed that theheavy quark contribution to inclusive cross sec-tions can be well accommodated in the dipolemodel approach.








B.15.5 Gluon saturation in forward ob-servables (J. Albacete, C. Marquet)

In [t10/073], we considered the forward di-hadron azimuthal correlations in d+Au colli-sions at RHIC. We studied the observed suppres-sion of the away-side peak in two-pions correla-tions at forward rapidities, showing that such aneect can be well described in the framework ofthe Color Glass Condensate.

In [t10/010], we studied the single inclusivehadron production in p+p and d+Au collisionsat RHIC. Here we presented a phenomenologi-cal analysis of available data in terms of the hy-brid formalism for forward production and un-integrated gluon distributions evolved accordingto the running coupling BK equation. With thisset up we provided a very good quantitative de-scription of the observed suppression of nuclearmodication factors in the forward region, thusproviding additional evidence for the importanceof non-linear, saturation eects in this kinematicregion.

B.15.6 CGC calculations for the Elec-tron Ion Collider

Future high-energy electron-ion colliders havebeen proposed (the EIC and LHeC) to, amongother things, investigate non-linear parton evo-lution in QCD. In this context, CGC calcula-tions for several deep inelastic scattering observ-ables have been performed.

Diractive structure functions (T. Lappi,C. Marquet)

In [t08/089], we have computed diractive struc-ture functions for both protons and nuclei in theframework of Color Glass Condensate modelswith impact parameter dependence. These mod-els have previously been shown to provide goodagreement with inclusive F2 measurements andexclusive vector meson measurements at HERA.For nuclei, they provide good (parameter free)agreement with the inclusive F2 data. We havedemonstrated the good agreement of our com-putations with HERA measurements on inclu-sive diraction. We also extended our analysisto nuclei and predicted the pattern of enhance-ment and suppression of the diractive struc-tures functions that can be measured at an Elec-tron Ion Collider. We showed that the impactparameter dependence crucially aects our anal-ysis, in particular for large invariant masses atxed Q2.

Semi-inclusive DIS (C. Marquet)

Semi-inclusive hadron production in deep inelas-tic scattering (SIDIS) was addressed [t09/097].It was shown that at small Bjorken x, this pro-cess provides a direct probe of the unintegratedgluon distribution. In particular, even at largevalues of photon virtualities, one is sensitive tothe saturation regime of the target wave func-tion, if the transverse momentum of the pro-duced hadron is of order of the saturation mo-mentum.

Diractive vector meson production onuclei (C. Marquet)

The crucial dierences between coherent dirac-tion (when the nucleus doesn't break-up) whichdominates at small momentum transfer, andincoherent diraction (when the nucleus scat-ters inelastically) which dominates at large mo-mentum transfer, have been investigated usingthe McLerran-Venugopalan model for the CGCwave function [t10/028].

B.15.7 Saturation scale from Wilson linecorrelators (T. Lappi)

In the color glass condensate framework the sat-uration scale measured in deep inelastic scatter-ing of high energy hadrons and nuclei can bedetermined from the correlator of Wilson linesin the hadron wavefunction. These same Wilsonlines give the initial condition of the classicaleld computation of the initial gluon multiplic-ity and energy density in a heavy ion collision.In [t07/146], the Wilson line correlator in bothadjoint and fundamental representations is com-puted using exactly the same numerical proce-dure that has been used to calculate gluon pro-duction in a heavy ion collision.

B.15.8 Factorization in the saturatedregime (F. Gelis, T. Lappi)

In the collision of two hadrons or nuclei athigh energy, in a regime where non linear ef-fects such as saturation are relevant, the stan-dard DGLAP or BFKL factorization frame-works fail to resum all the leading logarith-mic contributions. In a series of three papers[t08/068, t08/116, t08/232], we have proven thatone can still factorize all the leading logs of thecollision energy in the Color Glass Condensateframework, provided one considers sucientlyinclusive observables. In this factorization, thatin a sense generalizes the BFKL resummation byincluding all the non-linear corrections that arisein the high gluon density regime, the projectilesare described by functionals that represent their











color charge content and evolve with the factor-ization scale according to the JIMWLK equa-tion.

B.15.9 Multiplicity in nucleus-nucleuscollisions (J. Albacete, J.-P. Blaizot,F. Gelis, T. Lappi)

Semi-analytical results

In [t08/261], we show that a special choice oflight-cone gauge can greatly simplify the calcula-tion of the classical color eld created in the ini-tial stages of nucleus-nucleus collisions. Withinthis gauge, we can in particular construct ex-plicitly the conserved color current and calculateexactly the gauge eld immediately after the col-lision. This eld is used as a boundary conditionin an iterative solution of the Yang-Mills equa-tions in the forward light-cone. In leading order,which corresponds to a linearization of the Yang-Mills equation in the forward light-cone, we ob-tain a simple formula for the spectrum of gluonsproduced in nucleus-nucleus collisions. This for-mula reproduces exactly the known formula forproton-nucleus collisions, where kt-factorizationis recovered, while the latter property appar-ently breaks down in the case of nucleus-nucleuscollisions

In [t10/296], we study the gluon distributionin nucleus-nucleus collisions in the framework ofthe Color-Glass-Condensate. Approximate ana-lytical solutions are compared to numerical solu-tions of the non-linear Yang-Mills equations. Wend that the full numerical solution can be wellapproximated by taking the full initial conditionof the elds in Coulomb gauge and using a lin-earized solution for the time evolution. We alsocompare kt-factorized approximations to the fullsolution.

Multiplicity estimate for the LHC

In [t07/219], we have estimated the multiplic-ity of gluons expected in nucleus-nucleus colli-sions at the energy of the LHC, based on theCGC framework. The color charge distributionsof the colliding nuclei were evolved to the ap-propriate collision with the BK equation, witha simplistic implementation of running couplingeects. One word of caution is in order here:this framework strictly speaking describes whathappens at very short times after the collision,but not the subsequent fragmentation that mayoccur later in the evolution. This multiplicity istherefore a lower bound of the nal value, thatshould perhaps be increased if fragmentation issignicant in the nal state.

Complete multiplicity distribution

In [t09/063], we have extended the previousstudy by a calculation of all the higher momentsof the multiplicity distribution. We have foundthere that this distribution is approximately anegative binomial distribution, a fact that hadbeen observed in hadronic collisions at high en-ergy. To our knowledge, this is the rst deriva-tion of such a distribution in a framework thatcan be derived from QCD. Moreover, our studymakes a prediction for the dependence of the twoparameters that characterize the negative bino-mial distribution (the number of sources, andthe mean number of produced gluons per source)as a function of the collision energy and its im-pact parameter.

Eect of initial geometry uctuations

In [t10/313], we devised a model for initial gluonproduction in ultra-relativistic nucleus-nucleuscollisions at RHIC and the LHC based on theuse of unintegrated gluon distributions evolvedaccording to the running coupling BK evolutionand kt-factorization. Moreover, Monte Carlotechniques were employed to describe the uctu-ations in the collision geometry. Our predictionsagree very well with the data on total multiplic-ities measured in the rst Pb+Pb collisions atthe LHC, and also describe successfully existingRHIC data.

B.15.10 Two gluon correlations at largerapidity (F. Gelis, T. Lappi)

In [t09/124], we have analyzed the long rangerapidity correlations observed in the STAR ex-periment at RHIC. Our goal was to extract prop-erties of the two particle correlation matrix, ac-counting for the analysis method of the STARexperiment. We found a surprisingly large cor-relation strength for central collisions of gold nu-clei at highest RHIC energies. We argued thatsuch correlations cannot be the result of impactparameter uctuations.

In [t09/164], we have applied the above fac-torization results in a semiquantitative study ofthe double inclusive gluon spectrum. In this pa-per, we have shown that the CGC frameworkleads to a long-range rapidity correlation be-tween pairs of produced gluons, that reects thefact that QCD evolution in rapidity is signi-cant only over rapidity intervals of order 1/αs.Such correlations had in fact been observed ex-perimentally at RHIC, and this study has sincethen become the standard explanation of thislong range correlation.

Later, we have made this analysis more quan-









titative in [t10/067], where we calculated the ac-tual dependence of the correlation strength withthe rapidity separation between the two gluons(in the previous work, we had made approxi-mations that amounted to neglect this depen-dence). In fact, the real strength of the CGC isnot that it predicts a long range correlation (anysensible model of hadronic collisions should havesuch correlations), but that it provides a way toperform a rst principles calculation of the de-viation from a at correlation.

Finally, we have argued in [t10/149] thatsimilar correlations may also exist in proton-proton collisions, provided one triggers on eventsthat have an exceptionally large multiplicity.There is ongoing speculation that this eect maycontribute to the 2-hadron correlations observedrecently at the LHC by the CMS experiment.

B.15.11 Schwinger mechanism (F. Gelis,T. Lappi)

In [t09/104], we have developed a new methodfor deriving the (well-known) Schwinger mech-anism of pair production by an electrical eld.This derivation establishes a connection betweenthe Schwinger mechanism and particle produc-tion in the CGC framework at 1-loop order. Asa by-product, we obtained not only the meannumber of pairs produced by the electrical eld,but also all the higher moments and we couldconclude from this that the distribution of theproduced pairs is a coherent Bose-Einstein dis-tribution.

B.15.12 Thermal equilibration (F. Gelis,T. Epelbaum)

An outstanding problem in the application of theCGC framework to the description of heavy-ioncollisions is that of the thermalization of the glu-onic system produced in these collisions. Imme-diately after the collision, this system of gluonsis in a coherent state very far out-of-equilibrium,but experimental measurements tend to favor arather quick thermal equilibration.

In [t09/165], we made a rst attempt to re-late the CGC framework to a Boltzmann equa-tion. However, this has remained so far a for-mal exercise and was not pursued as a practicalway to study thermalization due to the technicalcomplexity of this Boltzmann equation.

A much more promising eort in this direc-tion is to resum a family of higher order cor-rections to the CGC picture, that is known togive secular divergences if considered at xed or-der. These divergences are closely related to in-stabilities and chaos in the classical Yang-Mills

equations, and to the known fact that they havepositive Lyapunov exponents. We have devel-oped a resummation procedure that collects theterms that have the most divergent behavior atevery loop order, and we have shown that theoutcome of this resummation is well behaved atany time. In [t10/148], we took this resumma-tion further in the simpler case of a scalar eldtheory, and implemented it numerically in orderto investigate its eect on the thermalization ofthe system. We have shown that it leads to arapid decay of the initial coherent state, and tothe relaxation of the pressure in the system toits equilibrium value.

B.15.13 Collisional meson dissociation(C. Marquet)

A 4-point function was computed which allowsto estimate the survival probability of a me-son propagating in the presence of cold or hotQCD matter [t08/226]. It was found that thisprobability decreases proportionally to the in-verse medium length instead of the exponen-tial law usually assumed in phenomenologicalstudies. This will be relevant when consider-ing the production of high-pT heavy mesons innucleus-nucleus collisions, as these can be pro-duced within the medium and their in-mediumdissociation will contribute to the strong sup-pression observed in heavy-ion collisions.

B.16 Central diractive processes(R. Peschanski)

In [t08/001], we propose a new set of measure-ments which can be performed at the LHC usingroman pot detectors. This new method is basedon exploiting excitation curves to measure kine-matical properties of produced particles. We il-lustrate it in the case of central diractive Wpair production.

In [t08/278], central diractive productionof heavy states (massive dijets, Higgs boson)is studied in the exclusive mode using a newHybrid Pomeron Model (HPM). Built from Hy-brid Pomerons dened by the combination of onehard and one soft color exchanges, the modeldescribes well the centrally produced diractivedijet data at the Tevatron. Predictions for theHiggs boson and dijet exclusive production atthe LHC are presented.

In [t08/071], exploiting the idea that the fastpartons of an energetic projectile can be treatedas sources of color radiation interpreted as weepartons, it is shown that the recently observedproperty of extended limiting fragmentation im-plies a scaling law for the rapidity distribution











of fast partons. This leads to a picture of a self-similar process where, for xed total rapidity Y,the sources merge with probability varying as1/y.

B.17 Gauge-gravity duality

In heavy ion experiments at RHIC, it has beenobserved that the quark-gluon plasma createdin these collisions behaves like an almost perfectuid, which could be explained if one assumesthat it is a system with strong coupling. Thismight be explained by the fact that the matterproduced in the collision is rapidly expandingand thus becomes dilute and potentially stronglycoupled.

These ndings raised the question of the the-oretical tools at our disposal for studying sucha strongly coupled form of matter. Such tech-niques had emerged a bit earlier in string theory,in the context of the gauge/string duality alsoknown as the AdS/CFT correspondence. In thisdescription, a gauge eld theory with conformalsymmetry and strong coupling the N = 4supersymmetric YangMills (SYM) theory isconjectured to be equivalent (dual) to a stringtheory that lives in a ten-dimensional space-timeand has weak coupling (thus it reduces to clas-sical gravity).

This approach has been used for qualita-tive studies of a strongly-coupled quark-gluonplasma, since QCD itself becomes nearly con-formal in the deconned phase at nite tem-perature. To obtain the dual of a nite-temperature plasma, one must insert a blackhole in the target space-time of the string theory.Using this approach, we have studied the prop-agation of `hard probes' (partons or jets withhigh energy and momentum) through a strongly-coupled plasma, with results to be detailed inwhat follows.

B.17.1 Parton picture at strong coupling(E. Iancu)

The observation at RHIC of a strong energyloss by partons (quarks and gluons) propagat-ing through the quark-gluon plasma a phe-nomenon known as `jet quenching' raisedthe question about the partonic structure ofhadronic system at strong coupling. Concep-tually, the most direct way to probe the struc-ture of a hadron at a hard resolution scale isto perform deep inelastic scattering (DIS), i.e.to scatter a virtual photon o that hadron.In a series of 4 publications, we have stud-ied the analogous problem at strong coupling,using the AdS/CFT correspondence, for three

dierent types of hadronic targets: a glue-ball in [t07/191], a nite-temperature plasma in[t07/192, t08/085], and a nucleus in [t09/171].These studies allowed us to deduce a picture forthe parton structure in a (conformal) gauge the-ory at strong coupling: via successive branching,the partons with relatively high energy dissoci-ate into new partons with lower energies, untilan equilibrium (or `saturation') state is reachedin which all the partons carry low fractions ofthe total energy (`low x') - the highest possiblevalue of x being xed by energy conservation.

This scenario bears some similarity with thephenomenon of gluon saturation at weak cou-pling, thus suggesting the universality of thisphenomenon, from weak to strong coupling.However, unlike what happens at weak coupling,where most of the hadron energy is carried bythe pointlike valence quarks, at strong couplingthere are no such constituents: all the partonsare soft and the hadron looks more like a jelly.A striking consequence of this picture is the ab-sence of hard jets in the nal state of a hypo-thetical collision at strong coupling. The nalstate would rather consist in an isotropic distri-bution of soft matter, as produced via successiveparton branching.

B.17.2 Langevin dynamics and jetquenching at strong coupling (E.Iancu)

On the basis of the above mentioned parton pic-ture, we have claried the mechanism for en-ergy loss and momentum broadening for a heavyquark immersed in a strongly-coupled plasma[t09/056]. Unlike at weak coupling, where thequark looses its energy predominantly via mul-tiple scattering o the medium constituents, atstrong coupling it does so via medium-inducedparton branching. This mechanism is encoded ina Langevin equation that we have derived fromAdS/CFT. Our construction has also interest-ing formal consequences: it establishes a `dual-ity' between the phenomenon of jet quenching ina gauge theory at strong coupling and the Un-ruh eect in the supergravity theory (the semi-classical limit of the string theory).

B.17.3 Heavy quark energy loss atstrong coupling (C. Marquet)

It was shown that, on the gravity side of the cor-respondence, energy loss is not due to a space-time event horizon, but rather to a string world-sheet horizon [t08/066]. On the gauge-theoryside, this horizon corresponds to the plasmasaturation scale that screens long-wave length








uctuations out of the quantum wave functionof the quark, which then loses the energy thatthose uctuations carry into the medium. Thisunderstanding in terms of a partonic pictureallowed to extend the existing gravity calcu-lations to estimate the thermalization time ofa heavy quark produced in a strongly-coupledSYM plasma [t08/223], as well as to infer therate of energy loss of a heavy quark in a nite-length plasma. The path length dependenceof the energy loss was found to be stronger inthe strong-coupling regime (proportional to thethird power of the path length) compared tothe weak-coupling regime (proportional to thesquare of the path length). In the prospect ofphenomenological studies, this important resulthas been incorporated inside a jet-quenching cal-culation [t09/122]. It was shown that modelingthe non-perturbative physics using the length-cubed law, instead of the length-squared lawas in standard calculations, improves the de-scription of the experimental data obtained inAu+Au collisions at RHIC.

B.17.4 A lattice test of the strong cou-pling hypothesis (E. Iancu)

In Ref. [t09/172] we proposed a lattice test ofthe strength of the coupling in QCD at nitetemperature. This consists in the lattice calcu-lation of the expectation value of a special `twist-two' operator which is orthogonal to the energy-momentum tensor in the sense of the renormal-ization group. This operator has a negativeanomalous dimension, so at strong coupling itsexpectation value should be strongly suppressedin the continuum limit.

B.17.5 Mesons in a strongly coupledplasma (E. Iancu)

In Ref. [t09/339] we have studied mesons(quark-antiquark bound states) in a plasma at -nite temperature and strong coupling. We havecomputed the corresponding spectral functionsand their contribution to the absorption of a vir-tual photon by the plasma. Interestingly, themeson dispersion relations become space-like inthe high momentum limit, showing that theirbinding energy grows as fast as the kinetic en-ergy when increasing the meson momentum.

B.17.6 Radiation at strong coupling: thequest for string uctuations (E.Iancu)

Very recently, we considered a conceptualproblem which deals with the foundations ofAdS/CFT, namely the importance of string uc-tuations. A central assumption prevailing since

the original papers by Maldacena and Wit-ten is that string uctuations are irrelevant inthe strong coupling limit. In Refs. [t10/289,t11/118] we showed via explicit examples thatthis is not always the case. By working in thesupergravity approximation, which ignores theseuctuations, we found that the AdS/CFT pre-dictions for observables like the radiation by ac-celerated sources in the vacuum of the N = 4SYM theory at strong coupling are incompati-ble with quantum mechanics. For instance, theenergy distribution produced by an acceleratedheavy quark, that we have exactly computed(in the supergravity approximation) for an arbi-trary quark motion [t11/118], exhibits the samespace-time pattern as the corresponding classi-cal distribution: the radiation propagates at thespeed of light without quantum broadening. Wehave then identied a class of string uctuationswhich do not decouple at strong coupling andwhich could restore the agreement between theresults of the string theory and our general phys-ical expectations [t10/289].

B.17.7 Viscosity of the QGP (R. Peschan-ski)

In [t07/189], we focus on challenging problemsof QGP hydrodynamics, such as viscosity andthermalization, in terms of gravitational dualsof both the static and relativistically evolvingplasma. We show how a Black Hole geometryarises naturally from the dual properties of anearly perfect uid and explore the lessons andprospects one may draw for actual heavy ioncollisions from the Gauge/Gravity duality ap-proach.

B.17.8 Early time dynamics (R. Peschan-ski)

In [t09/126], we study the boost-invariant dy-namics of a strongly-coupled conformal plasmain the regime of early proper-time using theAdS/CFT correspondence. It is shown, in con-trast with the late-time expansion, that a scalingsolution does not exist. The boundary dynam-ics in this regime depends on initial conditionsencoded in the bulk behavior of a Feerman-Graham metric coecient at initial proper-time.The relation between the early-time expansion ofthe energy density and initial conditions in thebulk of AdS is provided. As a general result itis proven that a singularity of some metric coef-cient in Feerman-Graham frame exists at alltimes. Requiring that this singularity at τ = 0is a mere coordinate singularity without the cur-vature blow-up gives constraints on the possible












boundary dynamics. Using a simple Pade re-summation for solutions satisfying the regular-ity constraint, the features of a transition to lo-cal equilibrium, and thus to the hydrodynamicallate-time regime, have been observed.

B.17.9 High energy bounds on N=4SYM amplitudes (R. Peschanski)

In [t09/299], we study the high-energy behav-ior of colorless dipole elastic scattering ampli-tudes in N=4 SYM gauge theory through theWilson loop correlator formalism and Euclideanto Minkowskian analytic continuation. Thepurely elastic behavior obtained at large impact-parameter L, through duality from disconnectedAdS5 minimal surfaces beyond the Gross-Ooguritransition point, is combined with unitarity andanalyticity constraints in the central region. Inthis way we obtain an absolute bound on thehigh-energy behavior of the forward scatteringamplitude due to the graviton interaction be-tween minimal surfaces in the bulk. The dom-inant Pomeron intercept is bounded by alphaless than or equal to 11/7 using the AdS/CFTconstraint of a weak gravitational eld in thebulk. Assuming the elastic eikonal approxima-tion in a larger impact-parameter range givesalpha between 4/3 and 11/7. The actual in-tercept becomes 4/3 if one assumes the elasticeikonal approximation within its maximally al-lowed range L larger than expY/3, where Y isthe total rapidity. Subleading AdS/CFT con-tributions at large impact-parameter due to theother d=10 supergravity elds are obtained. Adivergence in the real part of the tachyonic KKscalar is cured by analyticity but signals the needfor a theoretical completion of the AdS/CFTscheme.

B.17.10 Brane cosmology (R. Peschanski,P. Brax)

In [t10/239], we introduce a duality relationbetween two distinct branes, a cosmologicalbrane with macroscopic matter and a holo-graphic brane with microscopic gauge elds. Us-ing brane-world cosmology with a single branein a 5-dimensional AdS5 background, we ndan explicit time-dependent holographic corre-spondence between the bulk metric surround-ing the cosmological brane and the N=4 gaugeeld theory living on the boundary of the Z2-symmetric mirror bulk, identied with the holo-graphic brane. We then relate the cosmic accel-eration on the cosmological brane to the confor-mal anomaly of the gauge theory on the holo-graphic brane. This leads to a dual microscopic

interpretation of the number of e-foldings of thecosmological eras on the cosmological brane.

B.17.11 Hadrons in AdS/QCD models(C. Marquet)

On the application of the AdS/CFT dictionaryto model conning gauge theories at zero tem-perature, it was noticed that the additional free-dom at disposal to break conformal invariancecan always be used to reproduce all 2- and 3-point functions. Therefore it was investigated if4-point functions could be reproduced as well,this was done using electromagnetic propertiesof hadrons. In particular the Compton scatter-ing amplitude of a spin-less target was calculatedwithin the popular soft-wall model [t10/005],and serious limitations have been pointed out.

B.18 Relativistic hydrodynamicsExperiments at RHIC (Brookhaven) have shownthat the matter produced in a nucleus-nucleuscollision behaves like a uid. In this picture,particles are emitted independently, with someprobability distribution determined by the uidprole. This distribution is not azimuthallysymmetric: one usually denes anisotropic ows,vn, as the Fourier coecients of this probabilitydistribution vn ≡ |〈einϕ〉|, where ϕ is the az-imuthal angle, n is a positive integer, and angu-lar brackets denote an average value.

B.18.1 Flow extraction methods (J-Y. Ol-litrault)

vn can be inferred from azimuthal correlationsbetween outgoing particles. One diculty is toseparate correlations stemming from collectiveeects from other, nonow correlations. In ad-dition, the ow pattern is expected to uctuateevent by event: another diculty is to estimatethe magnitude of these ow uctuations. In thelast decade, we have developed a series of meth-ods (the cumulant method and the Lee-Yangzeroes method) which suppress nonow correla-tions and are now widely used. They were usedin particular in the rst analysis by the ALICEexperiment at LHC [arXiv:1011.3914]. However,most analyses at RHIC used an older method,the event-plane method. This method gives re-sults which always lie above estimates from 4-particle cumulants, and below estimates from 2-particle cumulants. We explain this dierencein [t09/047] (see also [t09/084]), by calculat-ing the sensitivity of the event-plane method tononow eects and ow uctuations. We showthat the result from the event-plane method isa well-dened interpolation between 2-particleand 4-particle cumulants, which does not give







any independent information. In another pa-per [t08/020], we show that the Lee-Yang-zeroesmethod can be seen as a slightly modied event-plane method.

B.18.2 The four lowest harmonics (J-Y.Ollitrault)

In November 2010, the ALICE collaborationpublished the rst measurement of elliptic ow(v2), the largest ow harmonic, in Pb-Pb colli-sions at the LHC [arXiv:1011.3914]. A few dayslater, Matt Luzum showed [t10/182] that theseresults were compatible with his earlier predic-tion using viscous hydrodynamics. Shortly be-fore the LHC started operating, several groupsindependently raised the possibility that ellipticow might even be present in proton-proton col-lisions at large multiplicities. In [t10/151], weestimated the magnitude of v2 in pp collisionsusing a partonic model of the proton based onQCD evolution. Our result is that azimuthalcorrelations from the parton evolution are likelyto be larger than correlations expected from el-liptic ow. We also nished an ongoing workpertaining to the interpretation of RHIC data:we showed in [t09/112] that the shear viscosity ofQCD can be extracted by comparing the mea-sured centrality dependence of v2 with viscoushydrodynamic calculations. The uncertainty re-mains large, and is dominated by uncertaintieson the initial density prole in the transverseplane.

Quadrangular ow, v4, has been measured byseveral collaborations at RHIC, but results werepoorly understood. Back in 2005, we had shownthat ideal hydrodynamics predicts v4 = 1

2 (v2)2,but data are consistently above this value. Ourrecent breakthrough was to recognize the im-portance of v2 uctuations [t09/152] (see also[t09/106, t09/245]), which explain most of thedeviation (there is a residual unexplained dis-crepancy for central collisions). We have alsocomputed v4 for the rst time using viscous hy-drodynamics [t10/060]. In viscous hydrodynam-ics, one needs to convert the uid into particlesat the end of the calculation, and there is somearbitrariness in this procedure. We have shownthat the procedure used by everyone so far failsbadly for v4 [t10/059], although it works well forv2.

A breakthrough was made in 2010 by Alverand Roland from MIT [arXiv:1003.0194], whorealized that several patterns seen in azimuthalcorrelations, known as ridge and shoulders, canbe interpreted simply as anisotropic ow in thethird harmonic, v3. Together with Alver, we

made the rst quantitative prediction for v3 us-ing viscous hydrodynamics [t10/095], and weshowed that this observable is more sensitive toviscosity than elliptic ow. Our prediction isin quantitative agreement with values inferredfrom STAR correlation data.

The last sizable harmonic, which is smallerthan the previous three, is v1. The possi-bility that initial uctuations followed by col-lective ow generate a nonzero v1 at midra-pidity was rst raised by Teaney and Yan[arXiv:1010.1876]. We have made a quantitativeprediction for this v1 using ideal hydrodynam-ics with uctuating initial conditions [t11/039].We had extracted v1 from published STAR cor-relation data [t10/185], and these measured val-ues are in excellent agreement with our hydro-dynamic calculation. We have also proposed aspecic method to analyze this v1 more accu-rately (also in [t10/185]).

B.18.3 Long-range correlations (J-Y. Ol-litrault)

Collective ow produces azimuthal correlationsbetween particles, even if they are separated by alarge rapidity gap. An important achievement ofour group is the recent recognition [t10/184] thatall the azimuthal patterns of these long rangecorrelations can in fact be explained by collec-tive ow, provided all four harmonics are takeninto account. We have proposed new ow ob-servables which can be constructed by correlat-ing up to ve particles in the rst three Fourierharmonics, and made quantitative prediction forthese observables [t11/110].

B.18.4 HBT interferometry (J-Y. Olli-trault)

In [t09/018] (see also [t09/099]), we have stud-ied another class of observables, namely, Bose-Einstein correlations between identical pions.These correlations are usually said to be sensi-tive probes of thermalization and ow. Therewas, however, a longstanding discrepancy be-tween hydrodynamics and experimental datafrom RHIC known as the HBT puzzle. Wehave calculated these correlations using a rel-ativistic Boltzmann equation in which one cantune the mean free path and vary the degreeof thermalization. We found that for realis-tic values of the mean free path, most of theHBT puzzle is automatically solved. Similarndings were reported independently by Pratt[arXiv:0811.3363] and other groups.



















B.18.5 Exact solutions (R. Peschanski)

In [t07/100], we have proposed a generaliza-tion of the Bjorken in-out Ansatz for uid tra-jectories which, when applied to the (1+1)-dimensional hydrodynamic equations, generatesa one-parameter family of analytic solutions in-terpolating between the boost-invariant Bjorkenpicture and the non boost-invariant one by Lan-dau. This parameter characterizes the proper-time scale when the uid velocities approach thein-out Ansatz.

In [t08/144], using the formalism of the Kha-latnikov potential, we have derived exact generalformulae for the entropy ow dS/dy, where y isthe rapidity, as a function of temperature for the(1+1)-d relativistic hydrodynamics of a perfectuid. We studied in particular ows dominatedby a suciently long hydrodynamic evolution,and provided an explicit analytical solution fordS/dy.

In [t10/033], looking for the underlying hy-drodynamic mechanisms determining the ellip-tic ow, we have showed that for an expandingrelativistic perfect uid the transverse ow mayderive from a solvable hydrodynamic potential,provided that the entropy is transversally con-served and the corresponding expansion quasi-stationary. Exact solutions for the velocity owcoecient v2 and the temperature dependence ofthe spatial and momentum anisotropy were ob-tained and were shown to be in agreement withthe elliptic ow features of heavy-ion collisions.

In [t10/210], we have presented a general so-lution of relativistic (1+1)-dimensional hydro-dynamics for a perfect uid owing along thelongitudinal direction as a function of time, uni-formly in transverse space. The Khalatnikov po-tential is expressed as a linear combination oftwo generating functions with polynomial coef-cients of 2 variables. These polynomials denean innite-dimensional basis of solutions. Thekinematics of the (1+1)-dimensional ow can bereconstructed from the potential.

In [t10/242], the possibility that particleproduction in high-energy collisions is a resultof two asymmetric hydrodynamic ows is in-vestigated, using the Khalatnikov form of the(1+1)-dimensional approximation of hydrody-namic equations. The general solution is dis-cussed and applied to the physically appealinggeneralized in-out cascade where the space-time and energy-momentum rapidities are equalat initial temperature but boost-invariance isnot imposed. It is demonstrated that the two-bump structure of the entropy density, charac-teristic of the asymmetric input, changes easily

into a single broad maximum compatible withdata on particle production in symmetric pro-cesses. A possible microscopic QCD interpre-tation of asymmetric hydrodynamics was pro-posed.

B.19 QFT at nite temperature

B.19.1 Heavy quarks in a quark-gluonplasma (J.-P. Blaizot)

Real and imaginary-time QQ correlators

In [t07/213], we investigate the behavior of apair of heavy fermions, denoted by Q and Q,in a hot/dense medium. Although we have inmind the situation where Q and Q denote heavyquarks, our treatment will be limited to sim-plied models, which bear only some generalsimilarities with QCD. We study in particularthe limiting case where the mass of the heavyfermions is innite. Then a number of resultscan be derived exactly: a Schrodinger equa-tion can be established for the correlator of theheavy quarks; the interaction eects exponenti-ate, leading to a simple instantaneous eectivepotential for this Schrodinger equation. We con-sider simple models for the medium in whichthe QQ pair propagates. In the case where themedium is a plasma of photons and light chargedfermions, an imaginary part develops in this ef-fective potential. We discuss the physical in-terpretation of this imaginary part in terms ofthe collisions between the heavy particles andthe light fermions of the medium; the same col-lisions also determine the damping rate of theheavy fermions. Finally we study the connectionbetween the real-time propagator of the heavyfermion pair and its Euclidean counterpart, andshow that the real part of the potential enter-ing the Schrodinger equation for the real-timepropagator is the free energy calculated in theimaginary-time formalism.

A path integral for heavy quarks in a hotplasma

In [t10/295], we propose a model for the prop-agation of a heavy-quark in a hot plasma, tobe viewed as a rst step towards a full descrip-tion of the dynamics of heavy quark systems in aquark-gluon plasma, including bound state for-mation. The heavy quark is treated as a nonrelativistic particle interacting with a uctuat-ing eld, whose correlator is determined by ahard thermal loop approximation. This approx-imation, which concerns only the medium inwhich the heavy quark propagates, is the onlyone that is made, and it can be improved. The









dynamics of the heavy quark is given exactlyby a quantum mechanical path integral that iscalculated in this paper in the Euclidean space-time using numerical Monte Carlo techniques.The spectral function of the heavy quark in themedium is then reconstructed using a MaximumEntropy Method. The path integral is also eval-uated exactly in the case where the mass ofthe heavy quark is innite; one then recoversknown results concerning the complex opticalpotential that controls the long time behaviorof the heavy quark. The heavy quark correla-tor and its spectral function are also calculatedsemi-analytically at the one-loop order, whichallows for a detailed description of the couplingbetween the heavy quark and the plasma collec-tive modes.

B.19.2 Exact renormalization group (J.-P. Blaizot)

Solutions of renormalization group owequations with full momentum depen-dence

In [t09/257], we demonstrate the power ofa recently-proposed approximation scheme forthe non-perturbative renormalization group thatgives access to correlation functions over theirfull momentum range. We solve numericallythe leading-order ow equations obtained withinthis scheme, and compute the two-point func-tions of the O(N) theories at criticality, in twoand three dimensions. Excellent results areobtained for both universal and non-universalquantities at modest numerical cost.

Exact renormalization group and Φ-derivable approximations

In [t10/292], we show that the so-called Φ-derivable approximations can be combined withthe exact renormalization group to provide e-cient non-perturbative approximation schemes.On the one hand, the Φ-derivable approxima-tions allow for a simple truncation of the in-nite hierarchy of the renormalization group owequations. On the other hand, the ow equa-tions turn the non linear equations that derivefrom the Φ-derivable approximations into an ini-tial value problem, oering new practical waysto solve these equations.

Pressure of a hot scalar theory within thenon-perturbative renormalization group

In [t10/294], we apply to the calculation of thepressure of a hot scalar eld theory a methodthat has been recently developed to solve theNon-Perturbative Renormalization Group. This

method yields an accurate determination of themomentum dependence of n-point functions overthe entire momentum range, from the low mo-mentum, possibly critical, region up to the per-turbative, high momentum region. It has there-fore the potential to account well for the con-tributions of modes of all wavelengths to thethermodynamical functions, as well as for theeects of the mixing of quasiparticles with multi-particle states. We compare the thermodynami-cal functions obtained with this method to thoseof the so-called Local Potential Approximation,and we nd extremely small corrections. Thisresult points to the robustness of the quasipar-ticle picture in this system. It also demon-strates the stability of the overall approxima-tion scheme, and this up to the largest valuesof the coupling constant that can be used in ascalar theory in 3+1 dimensions. This is in sharpcontrast to perturbation theory which shows nosign of convergence, up to the highest orders thathave been recently calculated.

B.19.3 Random matrices (J.-P. Blaizot)

Large Nc connement and turbulence

In [t08/260], we suggest that the transition thatoccurs at large Nc in the eigenvalue distributionof a Wilson loop may have a turbulent origin.We arrived at this conclusion by studying thecomplex-valued inviscid Burgers-Hopf equationthat corresponds to the Makeenko-Migdal loopequation, and we demonstrate the appearance ofa shock in the spectral ow of the Wilson loopeigenvalues. This picture supplements that ofthe Durhuus-Olesen transition with a particu-lar realization of disorder. The critical behaviorat the formation of the shock allows us to in-fer exponents that have been measured recentlyin lattice simulations by Narayanan and Neu-berger in d=2 and d=3. Our analysis leads us tospeculate that the universal behavior observedin these lattice simulations might be a genericfeature of connement, also in d=4 Yang-Millstheory.

Universal shocks in random matrix theory

In [t09/259], we link the appearance of univer-sal kernels in random matrix ensembles to thephenomenon of shock formation in some uiddynamical equations. Such equations are de-rived from Dyson's random walks after a properrescaling of the time. In the case of the GaussianUnitary Ensemble, on which we focus in this let-ter, we show that the orthogonal polynomials,and their Cauchy transforms, evolve accordingto a viscid Burgers equation with an eective







spectral viscosity νs = 1/2N , where N is thesize of the matrices. We relate the edge of thespectrum of eigenvalues to the shock that nat-urally appears in the Burgers equation for ap-propriate initial conditions, thereby obtaining anew perspective on universality.

B.19.4 Lattice QCD (R. Lacaze, A. Morel)

Eigenvalues and eigenvectors of the stag-gered Dirac operator

In [t08/052], we examine the eigenvalues andeigenvectors of the staggered Dirac operator onthermal ensembles created in QCD at nite tem-perature with two avours of dynamical stag-gered quarks. We make a numerical analy-sis of the cumulative distribution of eigenval-ues. In particular we see that across the phasetransition a gap opens in the spectrum, with aclear crossover from low to high temperature be-haviour evidenced by an increase in the lowesteigenvalue by three order of magnitude in theneighbourhood of Tc. To obtain additional in-sight on the gap formation, we analyse the lo-calization properties of the eigenvectors usingthe inverse participation ratio (IPR) and the lo-calization function. For nite volume latticesin the low-temperature phase the eigenvectorsare extended, but generic eld congurations inthe high temperature phase give rise to local-ized eigenstates. We examine measures of thestability of such localization and nd that at -nite volumes localization occurs through Mott'smechanism of the formation of mobility edges.However, the band gap between the localizedand extended states seem to scale to zero in thelimit of large volume.

Screening correlators with chiral fermions

In [t08/053], we study screening correlators ofquark-antiquark composites at T = 2Tc, whereTc is the QCD phase transition temperature, us-ing overlap quarks in the quenched approxima-tion of lattice QCD. As the lattice spacing ischanged from 1/4T to a = 1/6T and 1/8T , wend that screening correlators change little, incontrast with the situation for other types oflattice fermions. All correlators are close to theideal gas prediction at small separations. Thelong distance fallo is clearly exponential, show-ing that a parametrization by a single screeninglength is possible at distances z ≥ 1/T . Thecorrelator corresponding to the thermal vectoris close to the ideal gas value at all distances,whereas that for the thermal scalar deviates atlarge distances. This is examined through thescreening lengths and momentum space correla-

tors. There is strong evidence that the screeningtransfer matrix does not have reection positiv-ity.

Three dimensional nite temperatureSU(3) gauge theory

Three-dimensional SU(3) gauge theory shareswith QCD the existence of a transition betweena low temperature sector where the gauge de-grees of freedom are conned inside glueballs,and, above a critical temperature Tc, a phasewhere they behave as interacting elds asymp-totically free at large distances. This non per-turbative phenomenon is a consequence of theIR singularities of the perturbative expansion,in which fermionic matter elds do not partici-pate. Lattice simulations of SU(3) gauge theoryin 3 dimensions without quarks have been per-formed. Compared with QCD, the eect of theIR (UV) singularities is even stronger (weaker)and the computational eort much lighter, whilethe lessons drawn should be relevant to the re-alistic situation. In the large T/Tc region, thepressure P and the energy and entropy densi-ties of the gluon plasma have been measured forvarious lattice sizes and T/Tc < 15 [t08/214].The extrapolation to T/Tc =∞ of P/T 3 for thelargest lattices is close to the Stefan-Boltzmannlaw. For the same model, the correlation lengthbetween Polyakov loops have been measured in-side the conned phase and compared with theprediction of the bosonic string model [t09/280].Good agreement is found for T/Tc < 0.7, Asthe critical temperature is approached, the twovalues are not expected to agree anymore sincethe two models belong to dierent universalityclasses. More precise estimates of the correlationlength close to Tc are in progress.

B.19.5 Boundary eective theory (F. Ge-lis)

Calculations at nite temperature that involvelarge eld amplitudes become non perturba-tive, even if the coupling constant is small. In[t09/167], we have proposed a new way of reor-ganizing the perturbative expansion, dubbed theBoundary Eective Theory (BET), that is bet-ter behaved in these circumstances because itsbuilding blocks are classical elds. In [t11/137],we have used the BET in order to compute theeective potential in a scalar eld theory at nitetemperature. In this paper, we have shown thatthis eective theory leads to an eective poten-tial that smoothly interpolates between the well-known 1-loop result for small elds and a resultat large eld that deviates signicantly from the








classical action (due to large non-linear correc-tions).

B.20 Cold baryonic matter at highdensity and compact stars(M. Rho)

Baryonic matter at high density is a very poorlyunderstood strongly correlated system relevantto compact stars stable against gravitational col-lapse. It cannot be accessed by lattice QCD be-cause of the sign problem, there are no estab-lished model-independent theoretical tools, andat present no useful experimental data are avail-able. We address this problem relying on thefollowing three strategies [t10/017]: (i) hiddenlocal symmetry, (ii) large Nc and (iii) topol-ogy. Hidden local symmetry can be considered bottom-up as emergent from current alge-bras or as reduced top-down from string the-ory via holography. In both cases, topology g-ures in the structure of baryons as solitons, i.e.,skyrmions or instantons, in largeNc eective La-grangians. We present a variety of predictionsobtained in the approach that can impact onthe QCD phase structure, with hitherto unan-ticipated features of nuclear forces and nuclearstructure at high density, and on the equationof state (EoS) for compact stars.

B.20.1 Half-skyrmion matter

It has been discovered that when solitonsconstructed from hidden local symmetry La-grangian valid at large Nc, gauge-equivalent tononlinear sigma model extended to the scale cor-responding to the vector-meson mass, are put onan FCC crystal lattice so as to simulate densebaryonic matter, there is a phase transition froma skyrmion matter in FCC to a half-skyrmionmatter in CC at a density above that of nuclearmatter. This half-skyrmion matter is character-ized by vanishing quark condensate (〈qq〉 = 0)but non-zero pion decay constant. As such, itis not a chiral-symmetry restored state. It re-sembles the deconned quantum critical phasein condensed matter in which half-skyrmions be-come relevant degrees of freedom. There are nowell-dened order parameters here, so the pro-cess does not belong to the familiar Ginzburg-Landau-Wilson paradigm. This phase gives sev-eral novel predictions [t09/242] such as strongbinding of anti-kaons in nuclear matter, possiblyleading to the formation of dense kaonic nucleiand precocious kaon condensation in neutron-star matter. It also predicts a drastic modica-tion in nuclear tensor forces which will surely af-fect the nuclear symmetry energy at a high den-

sity relevant to compact stars [t10/068]. Thesefeatures could be tested at FAIR and JPARC.

B.20.2 Dilatons and the repulsive core

Implementing the trace anomaly of QCD to hid-den local symmetric theories requires the pres-ence of dilatons associated with broken confor-mal symmetry of QCD. Such a theory that com-bines hidden local symmetry and broken con-formal symmetry was constructed in [t08/010,t09/023]. Driving the matter described by sucha Lagrangian to chiral restoration at high den-sity can be eectuated by what is called dila-ton limit (DL) that leads to Weinberg's mendedsymmetry. It was found [t11/026] that as oneapproaches the DL, the vector mesons ρ andω decouple from the baryons. As a conse-quence, the famous hard-core repulsion presentat short internuclear distances conrmed inlattice QCD in matter-free space gets sup-pressed at high density, a prediction which hasnot yet been made in the literature. Further-more, the nuclear symmetry energy which is pro-portional to the square of the ρNN coupling willalso get suppressed. This mechanism was sug-gested as a means to understand the recentlydiscovered 1.97 solar-mass star the largest sofar measured with certainty PSRJ1614-2230.

B.20.3 Holographic dual QCD

The recent development on gravity-gauge du-ality has led to a low-energy eective theorythat is built with an innite tower of hidden lo-cal gauge elds. The holographic dual modelthat is closest to QCD is the Sakai-SugimotoD4/D8-D8 brane model. This model does not,however, have the ultraviolet completion corre-sponding to QCD, so is unlikely to work at veryshort distances, but it gives a fairly good de-scription of those meson properties that can bewell approximated by large Nc or, in the lat-tice language, in the quenched approximation.In [t07/017, t07/064], baryons that correspondto Witten's baryon vertex were constructed interms of the instantons of the 5D YM actionof Sakai and Sugimoto, and the eective actioncomprised of baryons and mesons in 5D so con-structed was found to be in surprisingly goodagreement with data, in fact better than the pre-vious skyrmion model.

One of the most notable results of this de-scription is that the vector (ρ,ω) dominance inhadron interactions, rst proposed in 1960's bySakurai, which has worked very well in the me-son sector but failed badly in the baryonic sec-tor, is recovered for both mesons and baryons in










terms of the innite tower of 4D vector mesons[t07/140]. It has been shown that the innite-tower structure can be captured in the nucleonform factors by a simple formula with two pa-rameters determined in the meson sector ofthe Sakai-Sugimoto model, giving a surprisinglygood agreement with experimental form factors[t11/025]. Together with other developments in-volving many-nucleon systems, this indicates avery important role that is played by the innitetower inherited from the bulk gravity sector.

In [t09/176], instanton baryons were put onan FCC crystal lattice in a way analogous toskyrmions to describe dense baryonic matter.Thanks to the innite tower structure of HLSelds, this approach comes out to be a lot morepowerful than the skyrmion approach. It wasfound that the instantons in FCC crystal frac-tionize at a density close to the half-skyrmiondensity into half-instantons in BCC, in the formof dyons in a salt conguration. This lends sup-port to the half-skyrmion structure with the van-ishing quark condensate discovered previously.

Describing dense hadronic matter in holo-graphic QCD without exploiting crystal struc-ture that agrees with nature turns out to beextremely dicult. Identifying the U(1) RNcharge in the bulk with baryonic density ofthe boundary sector which is often done bystring theorists gives a result that is totallyat odds with nature. An alternative model witha D4/D6 structure with a compact D6 baryonvertex was tried [t11/141] but it also failed.

B.20.4 Neutron stars and black holes

The possibility of kaon condensation in compact-star matter [t07/139] has implications on black-hole formations and hugely enhanced entropy inthe Universe. This aspect was discussed in lightof a possible connection to the cosmological nat-ural selection [t08/037].

The recent discovery of the 1.97 solar-massobject PSRJ1614-2230 was claimed to rule outthe possible softening associated with kaon con-densation invoked for black-hole formation. Itwas shown in [t11/024] that this claim is un-founded, that it is possible to have a three-layer compact-star structure consisting of nu-cleon matter, kaon condensed matter and quarkmatter that can accommodate∼ 2M stars witha radius ∼ 10 km and a central density of ∼ 10times the nuclear matter density, all consistentwith the observation.

B.21 Theoretical nuclear physics(B. Giraud)

B.21.1 Theory of fusion and ssion

Our work in this area is about practical ques-tions, such as the irradiation of thick materials,the synthesis of super-heavy elements by fusionof heavy ions, the use of the complex scalingmethod to predict resonances [t10/084, t09/090,t08/154, t08/095].

B.21.2 Theory of density functionals

This part of our activities deal with more for-mal mathematical methods, for a rigorous foun-dation of the nuclear density functional the-ory, including the important role played by nu-clear symmetries and the necessary inuence ofconcavity upon calculations of masses, densitiesand energy surfaces [t07/172, t08/014, t07/171,t10/057, t09/091, t09/207, t09/206, t07/174,t07/173].

Bibliography[t07/017] D.K. Hong, M. Rho, H.-U. Yee, and

P. Yi. Chiral Dynamics of Baryonsfrom String Theory. Phys. Rev. D, 76,061901(R), (2007), arXiv:hep-th/0701276.

[t07/064] D.K. Hong, M. Rho, H.-U. Yee, andP. Yi. Dynamics of Baryons from StringTheory and Vector Dominance. JHEP,0709, 063, (2007), arXiv:0705.2632.

[t07/100] A. Bialas, R.A. Janik, andR. Peschanski. Unied description ofBjorken and Landau 1+1 hydrodynam-ics. Phys. Rev. C, 76, 054901, (2007),arXiv:0706.2108.

[t07/107] W.T. Giele, D.A. Kosower, andZ. Skands P. A simple shower and match-ing algorithm. Phys. Rev. D, 78, 014026,(2008), arXiv:0707.3652.

[t07/110] M. Frigerio and E. Ma. Commonorigin of θ13 and ∆m2

12 in a model ofneutrino mass with quaternion symme-try. Phys. Rev. D, 76, 096007, (2007),arXiv:0708.0166.

[t07/113] M. Chemtob and P.N. Pandita. Im-plications of vacuum stability constraintson the nonminimal supersymmetric stan-dard model with lepton number viola-tion. Phys. Rev. D, 76, 095019, (2007),arXiv:0708.1284.

[t07/117] C.A. Savoy and A. Sil. Can Ina-tion Induce Supersymmetry Breaking in a





























Metastable Vacua ? Phys. Lett. B, 660,236239, (2008), arXiv:0709.1923.

[t07/122] F. Bernardeau, C. Grojean, andJ. Dalibard. Particle physics and cosmol-ogy: the fabric of spacetime. In Pro-ceedings de l'Ecole d'Ete de Physique desHouches, Session LXXXVI, 31 July-25August. Elsevier, (2007). Particle physicsand cosmology: the fabric of spacetime,Les Houches, 2006-08-25/2006-07-31.

[t07/123] G. Lavaux, R. Mohayaee, S. Colombi,B. Tully R., F. Bernardeau, and J. Silk.Observational biases in Lagrangian recon-structions of cosmic velocity elds. Mon.Not. R. Astron. Soc., 383, 12921318,(2008), arXiv:0707.3483.

[t07/139] G.E. Brown, C.-H. Lee, and M. Rho.Recent Developments on Kaon Conden-sation and Its Astrophysical Implica-tions. Phys. Rep., 462, 120, (2008),arXiv:0708.3137.

[t07/140] D.K. Hong, M. Rho, H.-U. Yee,and P. Yi. Nucleon Form Factorsand Hidden Symmetry in HolographicQCD. Phys. Rev. D, 77, 014030, (2008),arXiv:0710.4615.

[t07/141] C. Delaunay, C. Grojean, andJ. Wells. Dynamics of Non-renormalizableElectroweak Symmetry Breaking. JHEP,0804, 029, (2008), arXiv:0711.2511.

[t07/142] C. Caprini, R. Durrer, and G. Ser-vant. Gravitational wave generation frombubble collisions in rst-order phase tran-sitions: an analytic approach. Phys. Rev.D, 77, 124015, (2008), arXiv:0711.2593.

[t07/146] T. Lappi. Wilson line correlator in theMV model: relating the glasma to deepinelastic scattering. Eur. Phys. J. C, 55,285292, (2008), arXiv:0711.3039.

[t07/149] R. Contino and G. Servant. Discov-ering the top partners at the LHC us-ing same-sign dilepton nal states. JHEP,0806, 026, (2008), arXiv:0801.1679.

[t07/153] K. Agashe, A. Falkowski, I. Low, andG. Servant. KK Parity in Warped Ex-tra Dimension. JHEP, 0804, 027, (2008),arXiv:0712.2455.

[t07/156] L. Hollenstein, C. Caprini, R. Crit-tenden, and R. Maartens. Challenges

for creating magnetic elds by cosmic de-fects. Phys. Rev. D, 77, 063517, (2008),arXiv:0712.1667.

[t07/162] P. Valageas. Using the Zeldovich dy-namics to test expansion schemes. As-tron. Astrophys., 476, 3158, (2007),arXiv:0706.2593.

[t07/171] B.G. Giraud, Jennings B., and B.R.Barret. Existence of Density Functionalfor an Intrinsic State. Phys. Rev. A, 78,032507, (2008), arXiv:0707.3099.

[t07/172] B.G. Giraud. Density functionals inthe laboratory frame. Phys. Rev. C, 77,014311, (2008), arXiv:0707.3901.

[t07/173] B.R. Barrett, B.G. Giraud, B.K. Jen-nings, and P. Toberg N. Concavity for nu-clear binding, thermodynamical functionsand density functionals. Nucl. Phys. A,828, 267282, (2009), arXiv:0707.4096.

[t07/174] B.K. Jennings, B.R. Barrett, andB.G. Giraud. Bounds to binding ener-gies from the concavity of thermodynami-cal functions. (2008), arXiv:0708.3031.

[t07/175] P. Brax, C. van de Bruck, A.C.Davis, D.F. Mota, and D. Shaw. Testingchameleon theories with light propagatingthrough a magnetic eld. Phys. Rev. D,76, 085010, (2007), arXiv:0707.2801.

[t07/176] P. Brax, A.C. Davis, S.C. Davis,R. Jeannerot, and M. Postma. Warpingand F-term uplifting. JHEP, 0709, 125,(2007), arXiv:0707.4583.

[t07/177] P. Brax, C. van de Bruck, A.C. Davis,D.F. Mota, and D. Shaw. DetectingChameleons through Casimir Force Mea-surements. Phys. Rev. D, 76, 124034,(2007), arXiv:0709.2075.

[t07/178] P. Brax, A.C. Davis, S.C. Davis,R. Jeannerot, and M. Postma. D-termUplifted Racetrack Ination. JCAP, 0801,008, (2008), arXiv:0710.4876.

[t07/180] P. Brax, S.C. Davis, and M. Postma.The Robustness of ns < 0.95 in Race-track Ination. JCAP, 0802, 020, (2008),arXiv:0712.0535.

[t07/189] R. Peschanski. Quark-GluonPlasma/Black Hole duality fromGauge/Gravity Correspondence. vol-ume 110 of J. Phys.: Conf. Ser., 032014,(2008), arXiv:0710.0756.























[t07/191] Y. Hatta, E. Iancu, and A.H. Mueller.Deep inelastic scattering at strong cou-pling from gauge/string duality : the sat-uration line. JHEP, 0801, 026, (2008),arXiv:0710.2148.

[t07/192] Y. Hatta, E. Iancu, and A.H. Mueller.Deep inelastic scattering o a N=4 SYMplasma at strong coupling. JHEP, 0801,063, (2008), arXiv:0710.5297.

[t07/213] A. Beraudo, J.-P. Blaizot, andC. Ratti. Real and imaginary-timeQQ correlators in a thermal medium.Nucl. Phys. A, 806, 312338, (2008),arXiv:0712.4394.

[t07/217] C. Grojean. Higgsless approach toelectroweak symmetry breaking. C.R.Physique, 8, 10681077, (2007).

[t07/218] C. Grojean. New approaches to elec-troweak symmetry breaking. Physics-Uspekhi, 50, 135, (2007).

[t07/219] H. Fujii, F. Gelis, A.M. Stasto, andR. Venugopalan. Melting the ColorGlass Condensate at the LHC. (2007),arXiv:0707.1870.

[t08/001] M. Boonekamp, J. Cammin,R. Peschanski, and C. Royon. Thresholdscans in diractive W pair production viaQED processes at the LHC. Phys. Lett.B, 654, 104109, (2007), arXiv:0709.2742.

[t08/010] B.-Y. Park, M. Rho, and V. Vento.The Role of the Dilaton in Dense Skyr-mion Matter. Nucl. Phys. A, 807, 2837,(2008), arXiv:0801.1374.

[t08/014] B.G. Giraud. Scalar Nature of the Nu-clear Density Functional. Phys. Rev. C,78, 014307, (2008), arXiv:0801.3447.

[t08/015] M. Douspis, P.G. Castro, C. Caprini,and N. Aghanim. Optimising largegalaxy surveys for ISW detection. As-tron. Astrophys., 485, 395401, (2008),arXiv:0802.0983.

[t08/016] P. Valageas. Expansion schemes forgravitational clustering: computing two-point and three-point functions. As-tron. Astrophys., 484, 79101, (2008),arXiv:0711.3407.

[t08/020] A. Bilandzic, N.v.d. Kolk, J.-Y.Ollitrault, and R. Snellings. Event-plane ow analysis without non-ow ef-fects. Phys. Rev. C, 83, 014909, (2011),arXiv:0801.3915.

[t08/022] J.-P. Uzan, F. Bernardeau, andY. Mellier. Time drift of cosmological red-shifts and its variance. Phys. Rev. D, 77,021301, (2008), arXiv:0711.1950.

[t08/034] M. Cirelli, R. Franceschini, andA. Strumia. Minimal Dark Matter predic-tions for galactic positrons, anti-protons,photons. Nucl. Phys. B, 800, 204220,(2008), arXiv:0802.3378.

[t08/037] G.E. Brown, C.-H. Lee, andM. Rho. Kaon condensation, blackholes and cosmological natural selection.Phys. Rev. Lett., 101, 091101, (2008),arXiv:0802.2997.

[t08/045] Z. Bern, L.J. Dixon, D.A. Kosower,R. Roiban, M. Spradlin, C. Vergu, andA. Volovich. The Two-Loop Six-GluonMHV Amplitude in Maximally Supersym-metric Yang-Mills Theory. Phys. Rev. D,78, 045007, (2008), arXiv:0803.1465.

[t08/052] R.V. Gavai, S. Gupta, and R. Lacaze.Eigenvalues and Eigenvectors of the Stag-gered Dirac Operator at Finite Tempera-ture. Phys. Rev. D, 77, 114506, (2008),arXiv:0803.0182.

[t08/053] R.V. Gavai, S. Gupta, and R. La-caze. Screening correlators with chiralFermions. Phys. Rev. D, 78, 014502,(2008), arXiv:0803.1368.

[t08/054] C.F. Berger, Z. Bern, L.J. Dixon,F. Febres Cordero, D. Forde, H. Ita, D.A.Kosower, and D. Maitre. AutomatedImplementation of On-Shell Methods forOne-Loop Amplitudes. Phys. Rev. D, 78,036003, (2008), arXiv:0803.4180.

[t08/060] R. Peschanski. On the maximal noisefor stochastic and QCD travelling waves.Nucl. Phys. B [FS], 805, 377390, (2008),arXiv:0803.2626.

[t08/062] G. Beuf, R. Peschanski, C. Royon,and D. Salek. Systematic Analysis of Scal-ing Properties in Deep Inelastic Scatter-ing. Phys. Rev. D, 78, 074004, (2008),arXiv:0803.2186.























[t08/066] F. Dominguez, C. Marquet, A.H.Mueller, B. Wu, and B.-W. Xiao. Compar-ing energy loss and p⊥-broadening in per-turbative QCD with strong coupling N=4SYM theory. Nucl. Phys. A, 811, 197222,(2008), arXiv:0803.3234.

[t08/068] F. Gelis, T. Lappi, and R. Venu-gopalan. High energy factorization innucleus-nucleus collisions. 1. Phys. Rev.D, 78, 054019, (2008), arXiv:0804.2630.

[t08/069] A. Abada, P. Hosteins, F.-X. Josse-Michaux, and S. Lavignac. SuccessfulLeptogenesis in SO(10) Unication witha Left-Right Symmetric Seesaw Mecha-nism. Nucl. Phys. B, 809, 183217, (2009),arXiv:0808.2058.

[t08/070] M. Frigerio, P. Hosteins, S. Lavignac,and A. Romanino. A new, direct linkbetween the baryon asymmetry and neu-trino masses. Nucl. Phys. B, 806, 84102,(2009), arXiv:0804.0801.

[t08/071] A. Bialas, A. Bzdak, and R. Peschan-ski. Limiting fragmentation fromscale-invariant merging of fast par-tons. Phys. Lett. B, 665, 3538, (2008),arXiv:0804.2364.

[t08/084] E. Iancu, M.S. Kugeratski, and D.N.Triantafyllopoulos. Geometric Scaling inMueller-Navelet Jets. Nucl Phys. A, 808,95116, (2008), arXiv:0802.0343.

[t08/085] Y. Hatta, E. Iancu, and A.H. Mueller.Jet evolution in the N=4 SYM plasma atstrong coupling. JHEP, 0805, 037, (2008),arXiv:0803.2481.

[t08/089] H. Kowalski, T. Lappi, C. Marquet,and R. Venugopalan. Nuclear enhance-ment and suppression of diractive struc-ture functions at high energies. Phys. Rev.C, 78, 045201, (2008), arXiv:0805.4071.

[t08/095] R. Suzuki, T. Kruppa A., B.G. Gi-raud, and K. Kato. Continuum Level Den-sity of a Coupled Channel System in theComplex Scaling Method. Prog. Theor.Phys., 119, 949963, (2008).

[t08/106] S.D. Badger. Direct Extraction OfOne Loop Rational Terms. JHEP, 0901,049, (2009), arXiv:0806.4600.

[t08/110] E. Dudas, S. Lavignac, and J. Par-mentier. A light neutralino in hy-brid models of supersymmetry breaking.

Nucl. Phys. B, 808, 237259, (2009),arXiv:0808.0562.

[t08/116] F. Gelis, T. Lappi, and R. Venu-gopalan. High energy factorization innucleus-nucleus collisions 2 - Multigluoncorrelations. Phys. Rev. D, 78, 054020,(2008), arXiv:0807.1306.

[t08/117] C.F. Berger, Z. Bern, L.J. Dixon,F. Febres Cordero, D. Forde, H. Ita, D.A.Kosower, and D. Maitre. One-Loop Calcu-lations with BlackHat. volume 183 of Nucl.Phys. B (Proc. Suppl.), 313319, (2008),arXiv:0807.3705.

[t08/123] C.F. Berger, Z. Bern, L.J. Dixon,F. Febres Cordero, D. Forde, H. Ita, D.A.Kosower, and D. Maitre. One-Loop Multi-Parton Amplitudes with a Vector Bosonfor the LHC. (2008), arXiv:0808.0941.

[t08/126] F. Bazzocchi, M. Frigerio, andS. Morisi. Fermion masses and mix-ing in models with SO(10) x A4 symme-try. Phys. Rev. D, 78, 116018, (2008),arXiv:0809.3573.

[t08/139] M. Cirelli, M. Kadastik, M. Raidal,and A. Strumia. Model-independent im-plications of the e+, e-, anti-proton cos-mic ray spectra on properties of Dark Mat-ter. Nucl. Phys. B, 813, 121, (2009),arXiv:0809.2409.

[t08/144] G. Beuf, R. Peschanski, and E.N. Sari-dakis. Entropy ow of a perfect uid in(1+1) hydrodynamics. Phys. Rev. C, 78,064909, (2008), arXiv:0808.1073.

[t08/145] M. Chemtob. Contact interactionsin low scale string models with intersect-ing D6-branes. Phys. Rev. D, 78, 125020,(2008), arXiv:0808.1242.

[t08/154] Y. Abe, C. Shen, G. Kosenko, D. Boil-ley, and B.G. Giraud. Di-nucleus dynam-ics towards fusion of heavy nuclei. Int. J.Mod. Phys. E, 17, 22142220, (2008).

[t08/155] E. Babichev, P. Brax, C. Caprini,J. Martin, and D. Steer. Dirac Born In-feld (DBI) Cosmic Strings. JHEP, 0903,091, (2009), arXiv:0809.2013.

[t08/156] S.D. Badger, N.E.J. Bjerrum-Bohr,and P. Vanhove. Simplicity in the Struc-ture of QED and Gravity Amplitudes.JHEP, 0902, 038, (2009), arXiv:0811.3405.























[t08/160] F. Bernardeau and P. Valageas. Prop-agators in Lagrangian space. Phys. Rev.D, 78, 083503, (2008), arXiv:0805.0805.

[t08/161] F. Bernardeau, M. Crocce, andR. Scoccimarro. Multi-Point Propaga-tors in Cosmological Gravitational Insta-bility. Phys. Rev. D, 78, 103521, (2008),arXiv:0806.2334.

[t08/162] C. Pitrou, J.-P. Uzan, and F. Ber-nardeau. Cosmic microwave back-ground bispectrum on small angularscales. Phys. Rev. D, 78, 063526, (2008),arXiv:0807.0341.

[t08/163] M. Cirelli and A. Strumia. Min-imal Dark Matter predictions andthe PAMELA positron excess. vol-ume idm2008 of PoS, 089, (2008),arXiv:0808.3867. Identication of darkmatter 2008, Stockholm.

[t08/184] G. Bertone, M. Cirelli, A. Strumia,and M. Taoso. Gamma-ray and radio testsof the e+e- excess from DM annihilations.JCAP, 0903, 009, (2009), arXiv:0811.3744.

[t08/188] V. Gorini, U. Moschella, A.Y. Kamen-shchik, V. Pasquier, and A. Starobinsky.Tolman-Oppenheimer-Volko equations inpresence of the Chaplygin gas: stars andwormhole-like solutions. Phys. Rev. D, 78,064064, (2008), arXiv:0807.2740.

[t08/199] P. Valageas. Statistical properties ofthe Burgers equation with Brownian ini-tial velocity. J. Stat. Phys., 134, 589640,(2009), arXiv:0810.4332.

[t08/200] M. Cirelli. Non-standard neutrinosand Cosmology. volume 188 of Nucl. Phys.B (Proc. Suppl.), 339341, (2009). Neu-trino Oscillation Workshop, Conca Spec-chiulla, Otranto, Italie, 2008-09-06/2008-09-13.

[t08/201] P. Valageas. Ballistic aggregationfor one-sided Brownian initial veloc-ity. Physica A, 388, 10311045, (2009),arXiv:0812.2308.

[t08/214] P. Bialas, L. Daniel, A. Morel, andB. Petersson. Thermodynamics of SU(3)Gauge Theory in 2 + 1 Dimensions.Nucl. Phys. B, 807, 547565, (2009),arXiv:0807.0855.

[t08/220] B. Basso and G. Korchemsky. Non-perturbative scales in AdS/CFT. J. Phys.A, 42, 254005, (2009), arXiv:0901.4945.

[t08/223] G. Beuf, C. Marquet, and B.W.Xiao. Heavy-quark energy loss and ther-malization in a strongly coupled SYMplasma. Phys. Rev. D, 80, 085001, (2009),arXiv:0812.1051.

[t08/226] F. Dominguez, C. Marquet, andB. Wu. On multiple scatterings of mesonsin hot and cold QCD matter. Nucl. Phys.A, 823, 99119, (2009), arXiv:0812.3878.

[t08/227] A.C. Davis, P. Brax, and C. van deBruck. Brane Ination and Defect For-mation. Phil. Trans. R. Soc. A, Phys.Sci. Eng. (UK), A366, 28332842, (2008),arXiv:0803.0424.

[t08/228] P. Brax, C. van de Bruck, A.C. Davis,S.C. Davis, R. Jeannerot, and M. Postma.Racetrack ination with matter elds andcosmic strings. JCAP, 0807, 018, (2008),arXiv:0805.1171.

[t08/229] P. Brax, C. van de Bruck, A.C. Davis,and D. Shaw. f(R) Gravity and ChameleonTheories. Phys. Rev. D, 78, 104021,(2008), arXiv:0806.3415.

[t08/230] P. Brax, C.A. Savoy, and A. Sil. In-termediate Scale Ination and MetastableSupersymmetry Breaking. Phys. Lett. B,671, 374377, (2009), arXiv:0807.1569.

[t08/232] F. Gelis, T. Lappi, and R. Venu-gopalan. High energy factorization innucleus-nucleus collisions. 3. Long rangerapidity correlations. Phys. Rev. D, 79,094017, (2009), arXiv:0810.4829v2.

[t08/235] P. Brax, C. van de Bruck, L.M.H.Hall, and J.M. Weller. Slow-Roll Inationin the Presence of a Dark Energy Cou-pling. Phys. Rev. D, 79, 103508, (2009),arXiv:0812.2843.

[t08/251] D. Seery, S. Sloth, and F. Ver-nizzi. Inationary trispectrum from gravi-ton exchange. JCAP, 0903, 018, (2009),arXiv:0811.3934.

[t08/260] J.-P. Blaizot and M.A. Nowak.Large Nc connement and turbulence.Phys. Rev. Lett., 101, 102001, (2008),arXiv:0801.1859.

[t08/261] J.-P. Blaizot and Y. Mehtar-Tani.The classical eld created in early stagesof high energy nucleus-nucleus collisions.Nucl. Phys. A, 818, 97119, (2009),arXiv:0806.1422.
























[t08/271] C. Csaki, C. Delaunay, C. Grojean,and Y. Grossman. A Model of LeptonMasses from a Warped Extra Dimension.JHEP, 0810, 055, (2008), arXiv:0806.0356.

[t08/276] G. Brooijmans, A. Delgado, B.A. Do-brescu, C. Grojean, J. Alwall, K. Black,E. Boos, T. Bose, V. Bunichev, R. Con-tino, A. Djouadi, L. Dudko, Y. Ger-shtein, M. Gigg, M. Herquet, J. Hirn,G. Landsberg, K. Lane, E. Maina, A. Mar-tin, G. Moreau, M.M. Nojiri, A. Pukhov,P. Ribeiro, E. Ros, V. Sanz, H.J.Schreiber, G. Servant, E.H. Simmons,R.K. Singh, P. Skands, S. Su, T.M.P. Tait,M. Takeuchi, and M. Vos. New Physics atthe LHC: A Les Houches Report. Physicsat Tev Colliders 2007 New Physics Work-ing Group. (2010), arXiv:0802.3715.

[t08/278] R. Peschanski, M. Rangel, andC. Royon. Hybrid Pomeron Model ofexclusive central diractive production.Acta Phys. Pol. B, 40, 23232344, (2009),arXiv:0808.1691.

[t09/010] M. Cirelli and A. Strumia. Min-imal Dark Matter: model and re-sults. New J. Phys., 11, 105005, (2009),arXiv:0903.3381v1.

[t09/011] C. Caprini, R. Durrer, T. Konstandin,and G. Servant. General Properties of theGravitational Wave Spectrum from PhaseTransitions. Phys. Rev. D, 79, 083519,(2009), arXiv:0901.1661.

[t09/018] C. Gombeaud, T. Lappi, and J.-Y. Ol-litrault. Does interferometry probe ther-malization? Phys. Rev. C, 79, 054914,(2009), arXiv:0901.4908.

[t09/019] C.F. Berger, Z. Bern, L.J. Dixon,F. Febres Cordero, D. Forde, T. Gleisberg,H. Ita, D.A. Kosower, and D. Maitre. Pre-cise Predictions for W + 3 Jet Productionat Hadron Colliders. Phys. Rev. Lett., 102,222001, (2009), arXiv:0902.2760.

[t09/023] H.K. Lee and M. Rho. Dilatons inHidden Local Symmetry for Hadrons inDense Matter. Nucl. Phys. A, 829, 7699,(2009), arXiv:0902.3361.

[t09/027] C. Bräuninger and M. Cirelli. Anti-deuterons from heavy Dark Matter.Phys. Lett. B, 678, 2031, (2009),arXiv:0904.1165.

[t09/030] M. Cirelli and P. Panci. InverseCompton constraints on the Dark Mattere+e- excesses. Nucl. Phys. B, 821, 399416, (2009), arXiv:0904.3830.

[t09/031] C. Caprini, F. Finelli, D. Paoletti,and A. Riotto. The cosmic microwavebackground temperature bispectrum fromscalar perturbations induced by primor-dial magnetic elds. JCAP, 0906, 021,(2009), arXiv:0903.1420.

[t09/046] S. Galli, F. Iocco, G. Bertone, andA. Melchiorri. CMB constraints on darkmatter models with large annihilationcross section. Phys. Rev. D, 80, 023505,(2009), arXiv:0905.0003.

[t09/047] J.-Y. Ollitrault, A.M. Poskanzer, andS.A. Voloshin. Eect of ow uctua-tions and nonow on elliptic ow meth-ods. Phys. Rev. C, 80, 014904, (2009),arXiv:0904.2315.

[t09/054] E. Sefusatti. One-loop PerturbativeCorrections to the Matter and Galaxy Bis-pectrum with non-Gaussian Initial Condi-tions. Phys. Rev. D, 80, 123002, (2009),arXiv:0905.0717 [astro-ph.CO].

[t09/056] G. Giecold, E. Iancu, and A.H.Mueller. Stochastic trailing stringand Langevin dynamics from AdS/CFT.JHEP, 0907, 033, (2009), arXiv:0903.1840.

[t09/063] F. Gelis, T. Lappi, and L. McLerran.Glittering Glasmas. Nucl. Phys. A, 828,149160, (2009), arXiv:0905.3234.

[t09/065] M. Cirelli, F. Iocco, and P. Panci.Constraints on Dark Matter annihilationsfrom reionization and heating of the in-tergalactic gas. JCAP, 0910, 009, (2009),arXiv:0907.0719.

[t09/076] G. Korchemsky and E. Sokatchev.Symmetries and analytic properties ofscattering amplitudes in N=4 SYM the-ory. Nucl. Phys. B, 882, 151, (2010),arXiv:0906.1737.

[t09/078] C.F. Berger, Z. Bern, L.J. Dixon,F. Febres Cordero, D. Forde, T. Gleis-berg, H. Ita, D.A. Kosower, and D. Maitre.Next-to-Leading Order QCD Predictionsfor W+3-Jet Distributions at Hadron Col-liders. Phys. Rev. D, 80, 074036, (2009),arXiv:0907.1984.





















[t09/082] F. Iocco. An idea for detecting cap-ture dominated Dark Stars. volume 194of Nucl. Phys. B (Proc. Suppl.), 8285,(2009), arXiv:0906.4106. GGI 2009 con-ference on Dark Matter.

[t09/084] J.-Y. Ollitrault, A.M. Poskanzer, andS.A. Voloshin. Eect of nonow andow uctuations on elliptic ow meth-ods. volume 830 of Nucl. Phys. A, 279c282c, (2009), arXiv:0906.3463. 21st In-ternational Conference on UltrarelativisticNucleus-Nucleus collisions (Quark Mat-ter 2009), Knoxville, Tennessee, 2009-03-30/2009-04-04.

[t09/090] Y. Abe, C. Shen, D. Boilley, andB.G. Giraud. From Di-Nucleus to Mono-Nucleus - Neck Evolution in Fusion ofMassive Systems. Int. J. Mod. Phys. E,18, 21692174, (2009), arXiv:0901.0470.

[t09/091] B.G. Giraud and P. Moussa.Schroedinger equations for the squareroot density of an eigenmixture andthe square root of an eigendensity spinmatrix. Phys. Rev. C, 82, 024301, (2010),arXiv:0906.2668.

[t09/095] F. Chevallier, O. Kepka, C. Mar-quet, and C. Royon. Gaps between jetsat hadron colliders in the next-to-leadingBFKL framework. Phys. Rev. D, 79,094019, (2009), arXiv:0903.4598.

[t09/097] C. Marquet, B.-W. Xiao, andF. Yuan. Semi-inclusive Deep InelasticScattering at small x. Phys. Lett. B, 682,207211, (2009), arXiv:0906.1454.

[t09/099] C. Gombeaud, T. Lappi, and J.-Y.Ollitrault. Eects of partial thermal-ization on HBT interferometry. volume830 of Nucl. Phys. A, 817c820c, (2009),arXiv:0907.1392. The 21st InternationalConference on Ultra-Relativistic Nucleus-Nucleus Collisions (Quark Matter 2009),Knoxville, TN, 2009-03-30/2009-04-04.

[t09/102] G. Korchemsky and E. Sokatchev.Twistor transform of all tree amplitudesin N=4 SYM theory. Nucl. Phys. B, 829,478522, (2010), arXiv:0907.4107.

[t09/104] K. Fukushima, F. Gelis, and T. Lappi.Multiparticle correlations in the Schwingermechanism. Nucl. Phys. A, 831, 184214,(2009), arXiv:0907.4793.

[t09/106] C. Gombeaud and J.-Y. Ollitrault.Eects of ow uctuations and partialthermalization on v4. Phys. Rev. C, 81,014901, (2010), arXiv:0907.4664.

[t09/112] H. Masui, J.-Y. Ollitrault,R. Snellings, and A. Tang. The centralitydependence of ν2/ε: the ideal hydro limitand η/s. volume 830 of Nucl. Phys. A,463c466c, (2009), arXiv:0908.0403. The21st International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions(Quark Matter 2009), Knoxville, TN,2009-03-30/2009-04-04.

[t09/121] C. Caprini, R. Durrer, and G. Ser-vant. The stochastic gravitational wavebackground from turbulence and magneticelds generated by a rst-order phasetransition. JCAP, 0912, 024, (2009),arXiv:0909.0622.

[t09/122] C. Marquet and T. Renk. Jet quench-ing in the strongly-interacting quark-gluonplasma. Phys. Lett. B, 685, 270276,(2010), arXiv:0908.0880.

[t09/124] T. Lappi and L. McLerran. Longrange rapidity correlations as seen in theSTAR experiment. Nucl. Phys. A, 832,330345, (2009), arXiv:0909.0428.

[t09/126] G. Beuf, M.P. Heller, R.A. Janik, andR. Peschanski. Boost-invariant early timedynamics from AdS/CFT. JHEP, 0910,043, (2009), arXiv:0906.4423.

[t09/136] D. Maitre, C.F. Berger, Z. Bern,F. Febres Cordero, H. Ita, L.J. Dixon,D. Forde, T. Gleisberg, and D.A. Kosower.NLO QCD Predictions for W+3 jets.(2009), arXiv:0909.4949.

[t09/152] C. Gombeaud and J.-Y. Ollitrault.Why is v4/(v2)2 larger than predictedby hydrodynamics? volume 834of Nucl. Phys. A, 295c297c, (2010),arXiv:0910.0392. The 10th InternationalConference on Nucleus-Nucleus collisions,Beijing, China, 2009-08-16/2009-08-21.

[t09/154] M. Chemtob and P. Hosteins. Search-ing singlet extensions of the supersym-metric standard model in Z6−II orb-ifold compactication of heterotic string.Eur. Phys. J. C, 68, 539559, (2010),arXiv:0909.4497.




















[t09/158] L. Calibbi, M. Frigerio, S. Lavignac,and A. Romanino. Flavour violation insupersymmetric SO(10) unication with atype II seesaw mechanism. JHEP, 0912,057, (2009), arXiv:0910.0377.

[t09/164] A. Dumitru, F. Gelis, L. McLerran,and R. Venugopalan. Glasma ux tubesand the near side ridge phenomenon atRHIC. Nucl. Phys. A, 810, 91, (2008),arXiv:0804.3858.

[t09/165] F. Gelis, S. Jeon, and R. Venugopalan.How particles emerge from decaying clas-sical elds in heavy ion collisions: towardsa kinetic description of the Glasma. Nucl.Phys. A, 817, 61, (2009), arXiv:0706.3775.

[t09/167] A. Bessa, C.A. de Carvalho, E.S.Fraga, and F. Gelis. Semiclassical ther-modynamics of scalar elds. JHEP, 0708,007, (2007), arXiv:0705.1531.

[t09/169] C. Caprini, R. Durrer, and E. Fenu.Can the observed large scale magneticelds be seeded by helical primordialelds? JCAP, 0911, 001, (2009),arXiv:0906.4976.

[t09/171] E. Avsar, E. Iancu, L. McLerran,and D.N. Triantafyllopoulos. Shockwavesand deep inelastic scattering within thegauge/gravity duality. JHEP, 0911, 105,(2009), arXiv:0907.4604.

[t09/172] E. Iancu and A.H. Mueller. A latticetest of strong coupling behaviour in QCDat nite temperature. Phys. Lett. B, 681,247252, (2009), arXiv:0906.3175.

[t09/173] E. Avsar and E. Iancu. CCFMEvolution with Unitarity Corrections.Nucl. Phys. A, 829, 3175, (2009),arXiv:0906.2683.

[t09/174] E. Avsar and E. Iancu. BFKL andCCFM evolutions with saturation bound-ary. Phys. Lett. B, 673, 2429, (2009),arXiv:0901.2873.

[t09/176] M. Rho, S.-J. Sin, and I. Zahed. DenseQCD: a Holographic Dyonic Salt. Phys.Lett. B, 01, 077, (2010), arXiv:0910.3774.

[t09/178] P. Brun, G. Bertone, M. Cirelli,E. Moulin, J.-F. Glicenstein, F. Iocco, andL. Pieri. The cosmic ray lepton puzzle.Annual meeting of the French Astronomi-cal & Astrophysical Society (sf2a), (2009),arXiv:1001.5408.

[t09/179] P. Valageas. Some statistical proper-ties of the Burgers equation with white-noise initial velocity. J. Stat. Phys., 137,729764, (2009), arXiv:0903.0956.

[t09/180] P. Valageas. Quasi-linear regime andrare-event tails of decaying Burgers tur-bulence. Phys. Rev. E, 80, 016305, (2009),arXiv:0905.1910.

[t09/181] P. Valageas. Mass functions and biasof dark matter halos. Astron. Astrophys.,508, 93106, (2009), arXiv:0905.2277.

[t09/182] P. Valageas. Mass function and bias ofdark matter halos for non-Gaussian initialconditions. Astron. Astrophys., 514, A46,(2010), arXiv:0906.1042.

[t09/183] D. Munshi, P. Valageas, A. Cooray,and A. Heavens. Secondary non-Gaussianity and Cross-Correlation Analy-sis. Mon. Not. R. Astron. Soc., 414, 31733197, (2011), arXiv:0907.3229.

[t09/187] M. Cirelli, P. Panci, and D. Ser-pico P. Diuse gamma ray constraints onannihilating or decaying Dark Matter af-ter Fermi. Nucl. Phys. B, 840, 284303,(2010), arXiv:0912.0663.

[t09/199] P. Creminelli, G. D'Amico, J. Noreña,L. Senatore, and F. Vernizzi. Sphericalcollapse in quintessence models with zerospeed of sound. JCAP, 1004, 027, (2010),arXiv:0911.2701.

[t09/200] F. Bernardeau, C. Bonvin, and F. Ver-nizzi. Full-sky lensing shear at second or-der. Phys. Rev. D, 81, 083002, (2010),arXiv:0911.2244.

[t09/201] L. Boubekeur, P. Creminelli,G. D'Amico, J. Noreña, and F. Ver-nizzi. Sachs-Wolfe at second order:the CMB bispectrum on large angu-lar scales. JCAP, 0908, 029, (2009),arXiv:0906.0980.

[t09/202] P. Creminelli, G. D'Amico, J. Noreña,and F. Vernizzi. The Eective Theoryof Quintessence: the w<-1 Side Unveiled.JCAP, 0902, 018, (2009), arXiv:0811.0827.

[t09/206] B.G. Giraud and S. Karataglidis. Al-gebraic Density Functionals. Phys. Lett.B, 703 (1), 88, (2011), arXiv:0908.0593.

[t09/207] B.G. Giraud. Open Problems in Nu-clear Density Functional Theory. J. Phys.G, 37, 064002, (2010), arXiv:0911.5654.

























[t09/209] P. Brax, C. Burrage, A.C. Davis,D. Seery, and A. Weltman. Higgs pro-duction as a probe of dark energy inter-actions. Phys. Rev. D, 81, 103524, (2010),arXiv:0911.1267.

[t09/211] P. Brax, C. van de Bruck, J. Martin,and A.C. Davis. Decoupling Dark Energyfrom Matter. JCAP, 0909, 032, (2009),arXiv:0904.3471.

[t09/212] P. Brax, C. Burrage, A.C. Davis,D. Seery, and A. Weltman. Collider con-straints on interactions of dark energywith the Standard Model. JHEP, 0909,128, (2009), arXiv:0904.3002.

[t09/213] P. Brax, C.A. Savoy, and A. Sil.SQCD Ination & SUSY Breaking. JHEP,0904, 092, (2009), arXiv:0902.0972.

[t09/216] F. Bernardeau and P. Valageas. Eu-lerian and Lagrangian propagators forthe adhesion model (Burgers dynam-ics). Phys. Rev. D, 81, 043516, (2010),arXiv:0912.0356.

[t09/242] B.Y. Park, J.I. Kim, and M. Rho.Kaons in Dense Half-Skyrmion Mat-ter. Phys. Rev. C, 81, 035203, (2009),arXiv:0912.3213.

[t09/244] C. Pitrou, F. Bernardeau, and J.-P.Uzan. The y-sky: diuse spectral distor-tions of the cosmic microwave background.JCAP, 1007, 019, (2010), arXiv:0912.3655.

[t09/245] C. Gombeaud and J.-Y. Ollitrault.Are eccentricity uctuations able to ex-plain the centrality dependence of v4 ?volume 37 of J. Phys. G, 094024, (2010),arXiv:0912.3623. International Conferenceon Strangeness in Quark Matter (SQM09),Buzios, Brasil, 2009-09-27/2009-10-02.

[t09/250] F. Bernardeau and P. Valageas. Merg-ing and fragmentation in the Burgers dy-namics. Phys. Rev. E, 82, 016311, (2010),arXiv:0912.3603.

[t09/257] F. Benitez, J.-P. Blaizot, H. Chaté,B. Delamotte, R. Mendez-Galain, andN. Wschebor. Solutions of renormalizationgroup ow equations with full momentumdependence. Phys. Rev. E, 80, 030103(R),(2009), arXiv:0901.0128.

[t09/259] J.-P. Blaizot and M.A. Nowak. Uni-versal shocks in random matrix theory.Phys. Rev. E, 82, 051115 [6 pp.], (2010),arXiv:0902.2223v1.

[t09/264] P. Brax. Gif Lectures on Cosmic Ac-celeration. (2009), arXiv:0912.3610.

[t09/265] P. Brax and E. Cluzel. BraneBremsstrahlung in DBI Ination. JCAP,1003, 016, (2010), arXiv:0912.0806.

[t09/268] C.F. Berger, Z. Bern, L.J. Dixon,F. Febres Cordero, D. Forde, T. Gleis-berg, H. Ita, D.A. Kosower, and D. Maitre.Next-to-Leading Order Jet Physics withBlackHat. PoS RADCOR, 065, (2010),arXiv:0912.4927.

[t09/280] P. Bialas, L. Daniel, A. Morel, andB. Petersson. Three dimensional -nite temperature SU(3) gauge theory inthe conned region and the string pic-ture. Nucl. Phys. B, 836, 9199, (2010),arXiv:0912.0206.

[t09/284] G. Korchemsky. Surprising symmetryof scattering amplitudes in gauge theories.Mod. Phys. Lett. A, 24, 28682881, (2009).

[t09/285] M. Frigerio and T. Hambye. Darkmatter stability and unication withoutsupersymmetry. Phys. Rev. D, 81, 075002,(2010), arXiv:0912.1545.

[t09/293] M. Antonelli, D.M. Asner, D. Bauer,T. Becher, M. Beneke, A.J. Bevan,M. Blanke, C. Bloise, M. Bona, A. Bondar,C. Bozzi, J. Brod, A.J. Buras, N. Cabibbo,A. Carbone, G. Cavoto, M. Ciuchini, D.P.Cronin, C.H. Davies, J. Dingfelder, S. Do-nati, W. Dungel, U. Egede, G. Eigen,R. Faccini, T. Feldmann, P. Gambino,E. Gardi, T.J. Gershon, S. Giagu, T. Goto,C. Greub, C. Grojean, et al. FlavorPhysics in the Quark Sector. Phys. Rep.,494, 197414, (2010), arXiv:0907.5386.

[t09/294] A. De Roeck, J. Ellis, C. Grojean,et al. From the LHC to Future Collid-ers. Eur. Phys. J. C, 66, 525583, (2010),arXiv:0909.3240.

[t09/295] C. Grojean. New theories for theFermi scale. volume EPS-HEP of PoS,008, (2009), arXiv:0910.4976. EPS-HEPP'09 and Lepton-Photon 2009 confer-ences.

[t09/298] R. Peschanski. Traveling wavesolution of the Reggeon Field The-ory. Phys. Rev. D, 79, 105014, (2009),arXiv:0903.3373.























[t09/299] R. Peschanski and E.N. Saridakis. Ex-act hydrodynamic solution for the ellipticow. Phys. Rev. C, 80, 024907, (2009),arXiv:0906.0941.

[t09/302] R. Peschanski. Extended Geomet-ric Scaling from Generalized TravelingWaves. Phys. Rev. D, 81, 054014, (2010),arXiv:0912.1762.

[t09/315] C.B. Jackson, G. Servant, G. Shaugh-nessy, T.M.P. Tait, and M. Taoso. Higgsin Space! JCAP, 1004, 004, (2010),arXiv:0912.0004.

[t09/321] E. Sefusatti, M. Liguori, A. Ya-dav, P. S., G. Jackson, M., andE. Pajer. Constraining Running Non-Gaussianity. JCAP, 2009, 022067,(2009), arXiv:0906.0232.

[t09/332] R. Britto and B. Feng. Solvingfor tadpole coecients in one-loop ampli-tudes. Phys. Lett. B, 681, 376381, (2009),arXiv:0904.2766.

[t09/339] E. Iancu and A.H. Mueller. Light-like mesons and deep inelastic scatteringin nite-temperature AdS/CFT with a-vor. (2011), arXiv:0912.2238 [hep-th].

[t10/005] C. Marquet, C. Roiesnel, and S. Wal-lon. Virtual Compton Scattering o aSpinless Target in AdS/QCD. JHEP,1004, 51, (2010), arXiv:1002.0566.

[t10/007] J. Germer, W. Hollik, E. Mirabella,and K. Trenkel M. Hadronic productionof squark-squark pairs: the electroweakcontributions. JHEP, 1008, 023, (2010),arXiv:1004.2621.

[t10/010] L. Albacete J. and C. Marquet. SingleInclusive Hadron Production at RHIC andthe LHC from the Color Glass Conden-sate. Phys. Lett. B, 687, 174179, (2010),arXiv:1001.1378.

[t10/013] G. Korchemsky and E. Sokatchev. Su-perconformal invariants for scattering am-plitudes in N=4 SYM theory. Nucl. Phys.B, 839, 377419, (2010), arXiv:1002.4625.

[t10/017] W.G. Paeng and M. Rho. Toward aneective eld theory for cold compressedbaryonic matter. Mod. Phys. Lett. A, 25,399422, (2010), arXiv:1002.3022.

[t10/025] M. Cirelli, G. Corcella, A. Hek-tor, G. Hütsi, M. Kadastik, P. Panci,

M. Raidal, F. Sala, and A. Strumia. PPPTfor DMid: the Poor Particle PhysicistToolbox for Dark Matter indirect detec-tion. (2010), arXiv:1012.4515.

[t10/028] C. Marquet and H. Weigert. Newobservables to test the Color GlassCondensate beyond the large-Nc limit.Nucl. Phys. A, 843, 6897, (2010),arXiv:1003.0813.

[t10/031] R. Contino, C. Grojean, M. Moretti,F. Piccinini, and R. Rattazzi. Strong Dou-ble Higgs Production at the LHC. JHEP,1010, 5, (2010), arXiv:1002.1011.

[t10/032] C. Pitrou, J.-P. Uzan, and F. Bernar-deau. The cosmic microwave backgroundbispectrum from the non-linear evolutionof the cosmological perturbations. JCAP,1007, 003, (2010), arXiv:1003.0481.

[t10/033] M. Giordano and R. Peschanski. HighEnergy Bounds on Soft N=4 SYM Ampli-tudes from AdS/CFT. JHEP, 1005, 037,(2010), arXiv:1003.2309.

[t10/038] F. Bernardeau. Gravity and non-gravity mediated couplings in multiple-eld ination. Class. Quantum Grav., 27,124004, (2010), arXiv:1003.2869.

[t10/040] C.F. Berger, Z. Bern, L.J. Dixon,F. Febres Cordero, D. Forde, T. Gleis-berg, H. Ita, D.A. Kosower, and D. Maitre.Next-to-Leading Order QCD Predictionsfor Z, γ∗+3-Jet Distributions at the Teva-tron. Phys. Rev. D, D82, 074002, (2010),arXiv:1004.1659.

[t10/044] Z. Bern, J.J.M. Carrasco, and H. Jo-hansson. Perturbative Quantum Gra-vity as a Double Copy of Gauge The-ory. Phys. Rev. Lett., 105, 061602, (2010),arXiv:1004.0476.

[t10/057] B.R. Barret and B.G. Giraud. Spindensity matrices for nuclear density func-tionals with parity violations. (2010),arXiv:1004.4542.

[t10/058] K. Kong, K. Matchev, and G. Servant.Extra Dimensions at the LHC. Cambridge; New York : Cambridge University Press,(2010), arXiv:1001.4801.

[t10/059] M. Luzum and J.-Y. Ollitrault. Con-straining the viscous freeze out distribu-tion function with RHIC data. Phys. Rev.C, 82, 014906, (2010), arXiv:1004.2023.
























[t10/060] M. Luzum, C. Gombeaud, and J.-Y.Ollitrault. v4 in ideal and viscous hydro-dynamics for RHIC and LHC. Phys. Rev.C, 81, 054910, (2010), arXiv:1004.2024.

[t10/062] M. Cirelli and J.M. Cline. Can mul-tistate dark matter annihilation explainthe high-energy cosmic ray lepton anoma-lies? Phys. Rev. D, 82, 023503, (2010),arXiv:1005.1779.

[t10/065] C.F. Berger, D.A. Kosower, et al.Vector Boson + Jets with BlackHat andSherpa, (2010), arXiv:1005.3728.

[t10/066] F. Gelis, E. Iancu, J. Jalilian Mar-ian, and R. Venugopalan. The Color GlassCondensate. Annu. Rev. Nucl. Part. Sci.(submitted), (2010), arXiv:1002.0333.

[t10/067] K. Dusling, F. Gelis, T. Lappi,and R. Venugopalan. Long range two-particle rapidity correlations in A+A col-lisions from high energy QCD evolution.Nucl. Phys. A, 836, 159182, (2010),arXiv:0911.2720.

[t10/068] H.K. Lee, B.Y. Park, and M. Rho.Half-Skyrmions, Tensor Forces and Sym-metry Energy in Cold Dense Matter. Phys.Rev. C, (2010), arXiv:1005.0255.

[t10/071] C. Bonvin and C. Caprini. CMB tem-perature anisotropy at large scales inducedby a causal primordial magnetic eld.JCAP, 1005, 022, (2010), arXiv:1004.1405.

[t10/072] C. Caprini. Gravitational waves fromcosmological phase transitions. (2010),arXiv:1005.5291.

[t10/073] L. Albacete J. and C. Marquet.Azimuthal correlations of forward di-hadrons in d+Au collisions at RHIC inthe Color Glass Condensate. (2010),arXiv:1005.4065.

[t10/075] Z. Bern, J.J.M. Carrasco, L.J. Dixon,H. Johansson, and R. Roiban. CompleteFour-Loop Four-Point Amplitude in N=4Super-Yang-Mills Theory. Phys. Rev. D,82, 125040, (2010), arXiv:1008.3327.

[t10/084] Y. Abe, C. Shen, D. Boilley,G. Kosenko, and B.G. Giraud. Mechanismof Fusion Hindrance and Predictions ofSHE Production. Nucl. Phys. A, 834,349c352c, (2009).

[t10/086] Z. Bern, J.J.M. Carrasco, and H. Jo-hansson. The Structure of Multiloop Am-plitudes in Gauge and Gravity Theories.Nucl. Phys. B (Proc. Suppl.), 205-206, 5460, (2010), arXiv:1007.4297.

[t10/090] F. Bernardeau, M. Crocce, and E. Se-fusatti. Multi-Point Propagators for Non-Gaussian Initial Conditions. Phys. Rev. D,82, 083507, (2010), arXiv:1006.4656.

[t10/091] F. Alday, B. Eden, G. Korchemsky,E. Sokatchev, and J Maldacena. From cor-relation functions to Wilson loops. (2010),arXiv:1007.3243.

[t10/092] B. Eden, G. Korchemsky, andE. Sokatchev. From correlation func-tions to scattering amplitudes. (2010),arXiv:1007.3246.

[t10/094] A. Kaminska and S. Lavignac. Agauge-mediated supersymmetric littleHiggs model. (2010), arXiv:1007.2649.

[t10/095] B.H Alver, C. Gombeaud, M. Luzum,and J.-Y. Ollitrault. Triangular owin hydrodynamics and transport the-ory. Phys. Rev. C, 82, 034913, (2010),arXiv:1007.5469.

[t10/097] E. Dudas, S. Lavignac, and J. Par-mentier. Non-standard Susy spectra ingauge mediation. in: Proceedings of theXLVth Rencontres de Moriond on Elec-troWeak Interactions and Unied Theo-ries, La Thuile, Aosta Valley, Italy, 2010-03-06/2010-03-13, (2010).

[t10/098] M. Cirelli. Hoping to indirectly detectDark Matter with cosmic rays. CarpathianSummer School of Physics 2010, Sinaia,Romania, 2010-06-20/2010-07-03, (2010).

[t10/105] P. Brax, C. van de Bruck, A.C. Davis,and D. Shaw. Modifying Gravity atLow Redshift. JCAP, 1004, 032, (2010),arXiv:0912.0462.

[t10/111] C.F. Berger, Z. Bern, L.J. Dixon,F. Febres Cordero, D. Forde, T. Gleis-berg, H. Ita, D.A. Kosower, and D. Maitre.Precise Predictions for W + 4 Jet Pro-duction at the Large Hadron Collider.Phys. Rev. Lett., 106, 092001, (2011),arXiv:1009.2338.

[t10/114] F. Bernardeau. Mode coupling evolu-tion in arbitrary inationary backgrounds.JCAP, 02, 017, (2010), arXiv:1003.3575.
























[t10/120] C. Caprini, R. Durrer, andX. Siemens. Detection of gravitationalwaves from the QCD phase transitionwith pulsar timing arrays. Phys. Rev. D,82, 063511, (2010), arXiv:1007.1218.

[t10/139] B. Eden, G. Korchemsky, andE. Sokatchev. More on the dual-ity correlators/amplitudes. (2010),arXiv:1009.2488.

[t10/140] M. Liguori, E. Sefusatti, R. Fer-gusson, J., and E.P.S. Shellard. Pri-mordial non-Gaussianity and BispectrumMeasurements in the Cosmic MicrowaveBackground and Large-Scale Structure.(2010), arXiv:1001.4707.

[t10/141] E. Sefusatti, M. Crocce, and V. Des-jacques. The Matter Bispectrum inN-body Simulations with non-GaussianInitial Conditions. Mon. Not. R. As-tron. Soc., 406, 10141028, (2010),arXiv:1003.0007.

[t10/148] K. Dusling, T. Epelbaum, F. Gelis,and R. Venugopalan. Role of quantumuctuations in a system with strong elds:Onset of hydrodynamical ow. (2010),arXiv:1009.4363.

[t10/149] A. Dumitru, K. Dusling, F. Gelis,J. Jalilian Marian, T. Lappi, and R. Venu-gopalan. The ridge in proton-proton colli-sions at the LHC. (2010), arXiv:1009.5295.

[t10/151] E. Avsar, C. Flensburg, Y. Hatta,J.-Y. Ollitrault, and T. Ueda. Eccen-tricity and elliptic ow in proton-protoncollisions from parton evolution. (2011),arXiv:1009.5643.

[t10/167] M. Cirelli. Dark Matter, Cosmic Raysand Neutrinos: status circa 2010. Neu-trino Oscillation Workshop NOW 2010,Conca Specchiulla, Otranto, Italie, 2010-09-04/2010-09-11, (2010).

[t10/170] P. Valageas. Impact of shell crossingand scope of perturbative approaches inreal and redshift space. Astron. Astro-phys., 526, A67, (2011), arXiv:1009.0106.

[t10/171] P. Valageas and Takahiro Nishimichi.Combining perturbation theories withhalo models. Astron. Astrophys., 527, A87,(2011), arXiv:1009.0597.

[t10/172] P. Valageas. Large-scale bias of darkmatter halos. Astron. Astrophys., 525,A98, (2011), arXiv:1009.1131.

[t10/173] P. Valageas and F. Bernardeau. Den-sity elds and halo mass functions inthe Geometrical Adhesion toy Model.Phys. Rev. D, 83, 043508, (2011),arXiv:1009.1974.

[t10/175] E. Dudas, S. Lavignac, and J. Par-mentier. On messengers and metastabilityin gauge mediation. Phys. Lett. B, 698,162170, (2011), arXiv:1011.4001.

[t10/176] T. Konstandin and M. No J. Hydro-dynamic Obstructions in Bubble Expan-sions. (2010), arXiv:1011.3735.

[t10/182] M. Luzum. Elliptic ow at en-ergies available at the CERN LargeHadron Collider: Comparing heavy-iondata to viscous hydrodynamic predic-tions. Phys. Rev. C, 83, 044911, (2011),arXiv:1011.5173.

[t10/184] M. Luzum. Collective ow and long-range correlations in relativistic heavy ioncollisions. Phys. Lett. B, 696, 499504,(2011), arXiv:1011.5773.

[t10/185] M. Luzum and J.-Y. Ollitrault. Di-rected ow at midrapidity in heavy-ioncollisions. Phys. Rev. Lett., 106, 102301,(2011), arXiv:1011.6361.

[t10/195] F. Bernardeau, C. Pitrou, and J.-P.Uzan. CMB spectra and bispectra cal-culations: making the at-sky approxi-mation rigorous. JCAP, 02, 015, (2010),arXiv:1012.2652.

[t10/196] W.T. Giele, D.A. Kosower, andZ. Skands P. Higher-Order Corrections toTimelike Jets. (2010), arXiv:1102.2126.

[t10/197] L. Albacete J., N. Armesto, J.G.Milhano, P. Quiroga Arias, and A. Sal-gado C. AAMQS: A non-linear QCD anal-ysis of new HERA data at small-x includ-ing heavy quarks. (2010), arXiv:1012.4408[hep-ph].

[t10/205] P. Brax, J.F. Dufaux, and S. Mari-adassou. Preheating after Small-Field In-ation. Phys. Rev. D, 83, 103510, (2011),arXiv:1012.4656.

[t10/206] P. Brax and C. Burrage. AtomicPrecision Tests and Light Scalar Cou-plings. Phys. Rev. D, 83, 035020, (2011),arXiv:1010.5108.
























[t10/207] P. Brax, C. Burrage, A.C. Davis,D. Seery, and A. Weltman. Anomalouscoupling of scalars to gauge elds. Phys.Lett. B, 699, 59, (2011), arXiv:1010.4536.

[t10/209] P. Brax and C. Burrage. ChameleonInduced Atomic Afterglow. Phys. Rev. D,82, 095014, (2010), arXiv:1009.1065.

[t10/210] P. Brax and R. Peschanski.Gauge/Cosmology Brane-to-Brane Dual-ity. Acta Phys. Pol. B, 41, 26452667,(2010), arXiv:1006.3054.

[t10/211] P. Brax, C. van de Bruck, D.F.Mota, J. Nunes N., and A. Winther.Chameleons with Field Dependent Cou-plings. Phys. Rev. D, 82, 083503, (2010),arXiv:1006.2796.

[t10/212] P. Brax, C. van de Bruck, A.C. Davis,and D. Shaw. The Dilaton and ModiedGravity. Phys. Rev. D, 82, 063519, (2010),arXiv:1005.3735.

[t10/213] P. Brax, R. Rosenfeld, and D.A. Steer.Spherical Collapse in Chameleon Models.JCAP, 1008, 033, (2010), arXiv:1005.2051.

[t10/214] P. Brax and K. Zioutas. SolarChameleons. Phys. Rev. D, 82, 043007,(2010), arXiv:1004.1846.

[t10/215] P. Brax, C. van de Bruck, A.C. Davis,D. Shaw, and D. Iannuzzi. Tuning theMass of Chameleon Fields in CasimirForce Experiments. Phys. Rev. Lett., 104,241101, (2010), arXiv:1003.1605.

[t10/229] G. Zaharijas and A Abdo. Constraintson Cosmological Dark Matter Annihila-tion from the Fermi-LAT Isotropic DiuseGamma-Ray Measurement. JCAP, 1004,014, (2010), arXiv:1002.4415.

[t10/230] G. Zaharijas and M. Ackerman.Searches for Cosmic-Ray Electron Aniso-tropies with the Fermi Large Area Tele-scope. Phys. Rev. D, 82, 092003, (2010),arXiv:1008.5119.

[t10/237] J. Bros, H. Epstein, and U. Moschella.Scalar tachyons in the de Sitter universe.Lett. Math. Phys., 93, 203211, (2011),arXiv:1003.1396.

[t10/239] R. Peschanski and E.N. Saridakis. Ex-act (1+1)-dimensional ows of a perfectuid. (2011), arXiv:1006.1603.

[t10/242] A. Bialas and R. Peschanski. Asym-metric 1+1-dimensional hydrodynamics incollision. (2010), arXiv:1012.4687.

[t10/243] E. Dudas, v. Gersdor G., J. Parmen-tier, and S. Pokorski. Flavour in super-symmetry: horizontal symmetries or wavefunction renormalisation. JHEP, 1012,015, (2010), arXiv:1007.5208.

[t10/244] D. Langlois and F. Vernizzi. A ge-ometrical approach to nonlinear pertur-bations in relativistic cosmology. Class.Quantum Grav., 27, 124007, (2010),arXiv:1003.3270.

[t10/254] R. Britto and E. Mirabella. SingleCut Integration. JHEP, 1101, 135, (2011),arXiv:1011.2344.

[t10/257] R. Britto. Loop amplitudes in gaugetheories: modern analytic approaches.(2011), arXiv:1012.4493.

[t10/284] M. Beccaria, Dovier , G. Ma-corini, E. Mirabella, L. Panizzi, F.M. Re-nard, and C. Verzegnassi. Semi-inclusivebottom-Higgs production at LHC: Thecomplete one-loop electroweak eect in theMSSM. Phys. Rev. D, 82, 093018, (2010),arXiv:1005.0759.

[t10/289] Y. Hatta, E. Iancu, A.H. Mueller, andD.N. Triantafyllopoulos. Aspects of theUV/IR correspondence : energy broad-ening and string uctuations. (2011),arXiv:1011.3763 [hep-th].

[t10/292] J.-P. Blaizot, J.M. Pawlowski, andU. Reinosa. Exact renormalizationgroup and Φ-derivable approximations.Phys. Lett. B, 696, 523528, (2011),arXiv:1009.6048.

[t10/294] J.-P. Blaizot, A. Ipp, and N. Wsche-bor. Calculation of the pressure of a hotscalar theory within the Non-PerturbativeRenormalization Group. Nucl. Phys. A,849, 165181, (2011), arXiv:1007.0991v1.

[t10/295] A. Beraudo, J.-P. Blaizot, P. Facci-oli, and G. Garberoglio. A path inte-gral for heavy quarks in a hot plasma.Nucl. Phys. A, 846, 104142, (2010),arXiv:1005.1245v1.

[t10/296] J.-P. Blaizot, T. Lappi, andY. Mehtar-Tani. On the gluon spec-trum in the glasma. Nucl. Phys. A, 846,6382, (2010), arXiv:1005.0955v1.

























[t10/298] M. Cacciari, J. Rojo, G.P. Salam, andG. Soyez. Jet Reconstruction in Heavy IonCollisions. Eur. J. Phys., C, 1539, (2011),arXiv:1010.1759.

[t10/299] J.R. Espinosa, T. Konstandin, G. Ser-vant, and M. No J. Energy Budget of Cos-mological First-order Phase Transitions.JCAP, 1006, 028, (2010), arXiv:1004.4187.

[t10/300] M. Battaglia and G. Servant. Four-top production and tt + missing energyevents at multi TeV e+e− colliders. volumeC033 of Nuovo Cimento, 203208, (2010),arXiv:1005.4632. Linear Collider Work-shop 2009 (LC09), Perugia (Italie).

[t10/301] G. Servant. Four-top events at theLHC. Physics at the LHC 2010, DESY,Hambourg (Allemagne), 2010-06-07/2010-06-12, (2010).

[t10/302] C. Degrande, J.M. Gérard, C. Gro-jean, F. Maltoni, and G. Servant. Non-resonant New Physics in Top Pair Pro-duction at Hadron Colliders. JHEP, 1103,125, (2011), arXiv:1010.6304.

[t10/303] G. Servant. Dark matter at the elec-troweak scale: non-supersymmetric can-didates, 164189. Cambridge UniversityPress, (2010).

[t10/304] J.R. Espinosa, C. Grojean, andM. Muhlleitner. Composite Higgs Searchat the LHC. JHEP, 1005, 065, (2010),arXiv:1003.3251.

[t10/305] G. Brooijmans, C. Grojean, G.D.Kribs, and C. Shepherd-Themistocleous,editors. New Physics at the LHC. A LesHouches Report: Physics at TeV Collid-ers 2009, (2010), arXiv:1005.1229. LesHouches 2009, Physics at TeV Colliders,Les Houches, France, 2009-06-08/2009-06-26.

[t10/306] C. Grojean and M. Spiropulu, edi-tors. Proceedings of the 2009 CERN-Latin-American School of High-Energy Physics,(2010), arXiv:1010.5976. 5th CERN-LatinAmerican School of High-Energy Physics,Recinto Quirama, Colombia, 2009-03-15/2009-03-28.

[t10/307] C. Grojean and M. Spiropulu, edi-tors. Proceedings of the 2009 EuropeanSchool of High-Energy Physics, (2010),arXiv:1012.4643. 2009 European School

of High-energy Physics, Bautzen (Alle-magne), 2009-06-14/2009-06-27.

[t10/313] L. Albacete J. and A. Dumitru. Amodel for gluon production in heavy-ion collisions at the LHC with rcBKunintegrated gluon densities. (2010),arXiv:1011.5161 [hep-ph].

[t11/007] E. Sefusatti and F. Vernizzi. Cosmo-logical structure formation with cluster-ing quintessence. JCAP, 03, 047, (2011),arXiv:1101.1026.

[t11/021] J. Germer, W. Hollik, andE. Mirabella. Hadronic productionof bottom-squark pairs with electroweakcontributions. (2011), arXiv:1103.1258.

[t11/024] K. Kim, H.K. Lee, and M. Rho. DenseStellar Matter with Strange Quark Mat-ter Driven by Kaon Condensation. (2011),arXiv:1102.5167.

[t11/025] M. Harada and M. Rho. Integrat-ing Holographic Vector Dominance to Hid-den Local Symmetry for the Nucleon FormFactor. (2011), arXiv:1102.5489.

[t11/026] C. Sasaki, H.K. Lee, W.G. Paeng,and M. Rho. Conformal anomaly and thevector coupling in dense matter. (2011),arXiv:1103.0184.

[t11/029] J.J.M. Carrasco and H. Johansson.Generic Multiloop Methods and Applica-tion to N = 4 Super-Yang-Mills. (2011),arXiv:1103.3298.

[t11/032] M. No J. Large GravitationalWave Background Signals in Elec-troweak Baryogenesis Scenarios. (2011),arXiv:1103.2159.

[t11/034] A.V. Belitsky, G. Korchemsky, andE. Sokatchev. Are scattering amplitudesdual to super Wilson loops? (2011),arXiv:1103.3008.

[t11/036] B. Eden, P. Heslop, G. Korchem-sky, and E. Sokatchev. The super-correlator/super-amplitude duality: PartI. (2011), arXiv:1103.3714.

[t11/037] B. Eden, P. Heslop, G. Korchem-sky, and E. Sokatchev. The super-correlator/super-amplitude duality: PartII. (2011), arXiv:1103.4353.























[t11/039] F.G. Gardim, F. Grassi, Y. Hama,M. Luzum, and J.-Y. Ollitrault. Directedow at mid-rapidity in event-by-event hy-drodynamics. Phys. Rev. C, 83, 064901,(2011), arXiv:1103.4605.

[t11/040] Z. Bern, L.J. Dixon,F. Febres Cordero, g. diana, D. Forde,T. Gleisberg, S. Hoeche, H. Ita, D.A.Kosower, D. Maitre, and K. Ozeren.Left-Handed W Bosons at the LHC.(2011), arXiv:1103.5445.

[t11/051] D. Jeong, F. Schmidt, and E. Se-fusatti. Primordial Non-Gaussianity andthe Statistics of Weak Lensing andother Projected Density Fields. (2011),arXiv:1104.0926.

[t11/064] C. Caprini. Limits for primordialmagnetic elds. (2011), arXiv:1103.4060.

[t11/075] Z. Huang. The Art of Lattice andGravity Waves from Preheating. (2011),arXiv:1102.0227.

[t11/099] F. Bernardeau and P. Brax. Cosmo-logical Large-scale Structures beyond Lin-ear Theory in Modied Gravity. JCAP,06, 019, (2011), arXiv:1102.1907.

[t11/110] R.S. Bhalerao, M. Luzum, andJ.-Y. Ollitrault. Determining initial-state uctuations from ow measure-ments in heavy-ion collisions. (2011),arXiv:1104.4740.

[t11/112] P. Brax and E. Cluzel. PerturbationTheory in k-Ination Coupled to Matter.JCAP, 1104, 014, (2011), arXiv:1102.1917.

[t11/113] P. Brax, C. van de Bruck, A.C. Davis,B. Li, and D. Shaw. Nonlinear Struc-ture Formation with the EnvironmentallyDependent Dilaton. Phys. Rev. D, 83,104026, (2011), arXiv:1102.3692.

[t11/118] Y. Hatta, E. Iancu, A.H. Mueller, andD.N. Triantafyllopoulos. Radiation by a

heavy quark in N=4 SYM at strong cou-pling. (2011), arXiv:1102.0232 [hep-th].

[t11/122] C.A. Savoy and M. Thormeier. Ex-otic particles below the TeV from low scaleavour theories. JHEP, 1103, 128, (2011),arXiv:1003.2090.

[t11/125] G. Soyez. A simple description of jetcross-section ratios. Phys. Lett. B, 5962,(2011), arXiv:1101.2665.

[t11/126] M. Cacciari, G.P. Salam, andG. Soyez. Fluctuations and asymmetricjet events in PbPb collisions at the LHC.(2011), arXiv:1101.2878.

[t11/128] C. Degrande, J.M. Gérard, C. Gro-jean, F. Maltoni, and G. Servant. Aneective approach to same sign top pairproduction at the LHC and the forward-backward asymmetry at the Tevatron.(2011), arXiv:1104.1798.

[t11/129] T. Konstandin and G. Servant. Cos-mological Consequences of Nearly Confor-mal Dynamics at the TeV scale. (2011),arXiv:1104.4791.

[t11/130] T. Konstandin and G. Servant. Natu-ral Cold Baryogenesis from Strongly Inter-acting Electroweak Symmetry Breaking.(2011), arXiv:1104.4793.

[t11/131] C. Grojean, E. Salvioni, and R. Torre.A weakly constrained W' at the earlyLHC. (2011), arXiv:1103.2761.

[t11/137] A. Bessa, C.A. de Carvalho, E.S.Fraga, and F. Gelis. Eective poten-tial in the BET formalism. (2011),arXiv:1104.1084.

[t11/141] K. Jo, M. Rho, S.-J. Sin, andY. Seo. The dropping of in-mediumhadron mass in holographic QCD. (2011),arXiv:1104.2362.





















CHAPTERC

Statistical physics and condensed matter

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

C.1 Fluctuation theorems and related identities . . . . . . . . . . . . . . 139

C.1.1 Fluctuation theorems and work identities . . . . . . . . . . . . . . . . . 139

C.1.2 Maximization of the Shannon entropy of dynamical trajectories . . . . . 139

C.1.3 A meaningful expansion around detailed balance . . . . . . . . . . . . . 139

C.1.4 The modied SutherlandEinstein relation for diusive nonequilibria . . 140

C.1.5 Monotone return to steady nonequilibrium . . . . . . . . . . . . . . . . 140

C.2 Exactly solvable models out of equilibrium . . . . . . . . . . . . . . . 140

C.2.1 Some exactly solvable models out of equilibrium . . . . . . . . . . . . . 140

C.2.2 Large deviations of the current in the exclusion process . . . . . . . . . 141

C.2.3 Algebraic properties of a disordered asymmetric Glauber model . . . . . 142

C.2.4 On some classes of open two-species exclusion processes . . . . . . . . . 142

C.2.5 The spectrum of an asymmetric annihilation process . . . . . . . . . . . 142

C.2.6 Phase diagram of the ABC model on an interval . . . . . . . . . . . . . 142

C.2.7 Non equilibrium stationary states and phase transitions in directed Isingmodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

C.3 Stochastic processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

C.3.1 Longest excursion of stochastic processes in nonequilibrium systems . . 143

C.3.2 Random walk and related stochastic processes . . . . . . . . . . . . . . 143

C.3.3 Do solids ow? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

C.3.4 Slow annealing through critical points: the Kibble-Zurek mechanism re-visited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

C.3.5 First passage in innite paraboloidal domains . . . . . . . . . . . . . . . 144

C.3.6 Zero-temperature dynamics in the 3d Ising-Glauber model . . . . . . . . 145

C.3.7 A light impurity in an equilibrium gas . . . . . . . . . . . . . . . . . . . 145

C.3.8 Accelerated sampling of Boltzmann distributions . . . . . . . . . . . . . 146

C.3.9 Accelerated stochastic sampling of discrete statistical systems . . . . . . 146

C.4 Glass physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

C.4.1 A theoretical perspective on the glass transition and nonequilibrium phe-nomena in disordered materials . . . . . . . . . . . . . . . . . . . . . . . 146

C.4.2 Dynamical heterogeneity in glasses, colloids and granular materials . . . 146

C.4.3 Lattice models and the glass transition . . . . . . . . . . . . . . . . . . . 146

C.4.4 Theory of the glass transition: random rst order transition . . . . . . . 147

C.4.5 Theory of the glass transition: mode coupling theory . . . . . . . . . . . 147

C.4.6 Dynamical heterogeneity in super-cooled liquids . . . . . . . . . . . . . . 147

C.4.7 Glassy dynamics as a melting process . . . . . . . . . . . . . . . . . . . 147

131


C.4.8 Aging is - almost - like equilibrium . . . . . . . . . . . . . . . . . . . . . 148

C.5 Granular media and the jamming transition . . . . . . . . . . . . . . 148

C.5.1 Jamming transition of granular materials and relationship with glassydynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

C.5.2 Slow dynamics of a granular column . . . . . . . . . . . . . . . . . . . . 148

C.6 Spin glasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

C.6.1 The nature of the spin glass phase in low dimension . . . . . . . . . . . 149

C.6.2 Finite size scaling in the SK model . . . . . . . . . . . . . . . . . . . . . 149

C.6.3 Distribution of relaxation time in the SK model . . . . . . . . . . . . . . 150

C.6.4 Large random correlations in individual mean eld spin glass sample . . 150

C.6.5 Spin glass phase in random eld Ising model, possible or not . . . . . . 150

C.7 Other disordered systems . . . . . . . . . . . . . . . . . . . . . . . . . 150

C.7.1 Phase transitions of random systems . . . . . . . . . . . . . . . . . . . . 150

C.7.2 Disorder-dominated phases of random systems . . . . . . . . . . . . . . 150

C.7.3 Random walks in random media . . . . . . . . . . . . . . . . . . . . . . 151

C.7.4 Non-equilibrium dynamics of disordered systems . . . . . . . . . . . . . 151

C.8 Hard optimization problems . . . . . . . . . . . . . . . . . . . . . . . . 151

C.9 Networks, theoretical epidemiology, quantitative urbanism . . . . . 151

C.9.1 Spatial networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

C.9.2 Fluctuation eects in metapopulation models: percolation and pandemicthreshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

C.9.3 Disentangling collective trends from local dynamics . . . . . . . . . . . . 152

C.9.4 Structure of urban movements: polycentric activity and entangled hier-archical ows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

C.9.5 Fluctuations, records, and leaders in growing network models . . . . . . 153

C.10 Heavy fermion physics . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

C.10.1 The modulated spin liquid in URu2Si2 . . . . . . . . . . . . . . . . . . . 153

C.10.2 Kondo breakdown in 3He bi-layers . . . . . . . . . . . . . . . . . . . . . 154

C.10.3 Kondo breakdown and selective Mott transition in heavy fermions . . . 154

C.11 High temperature superconductors and Mott transition . . . . . . . 155

C.11.1 Cuprate superconductors . . . . . . . . . . . . . . . . . . . . . . . . . . 155

C.11.2 Iron-based superconductors . . . . . . . . . . . . . . . . . . . . . . . . . 156

C.11.3 Eect of crystal eld splitting on the Mott transition . . . . . . . . . . . 156

C.12 Antiferromagnets and spin liquids . . . . . . . . . . . . . . . . . . . . 156

C.12.1 Classical frustrated spin systems . . . . . . . . . . . . . . . . . . . . . . 156

C.12.2 Quantum dimer models . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

C.12.3 Quantum spin liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

C.12.4 The valence bond glass phase . . . . . . . . . . . . . . . . . . . . . . . . 157

C.12.5 Dimers on the cubic lattice . . . . . . . . . . . . . . . . . . . . . . . . . 157

C.12.6 Vacancy localization in the square dimer model . . . . . . . . . . . . . . 157

C.13 Ultra-cold atomic gases . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

C.13.1 Fermionic Mott transition . . . . . . . . . . . . . . . . . . . . . . . . . . 158

C.13.2 Polarized superuidity in the attractive Hubbard model with populationimbalance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

C.14 Graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

C.14.1 Graphene fundamental physics . . . . . . . . . . . . . . . . . . . . . . . 158

C.14.2 Eects of impurity scattering in graphene on the local density of states 158

C.14.3 Modied graphene and graphene-related materials . . . . . . . . . . . . 158

C.15 Bosonic systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

C.15.1 Super-solidity in He4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

C.15.2 Bose Einstein condensation of magnons . . . . . . . . . . . . . . . . . . 159

C.16 Out of equilibrium dynamics of quantum systems . . . . . . . . . . . 159

C.16.1 Quantum out of equilibrium dynamics . . . . . . . . . . . . . . . . . . . 159

Statistical physics and condensed matter 133

C.16.2 Thermalization of isolated quantum systems . . . . . . . . . . . . . . . . 160

C.16.3 Quantum phase space Brownian motion, a simple open system . . . . . 160

C.17 Quantum entanglement . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

C.17.1 Entanglement of two disjoint intervals in a spin chain . . . . . . . . . . 160

C.17.2 Entanglement in Rokhsar-Kivelson wave-functions and Shannon entropyof spin chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

C.17.3 Fidelity in critical spin chains . . . . . . . . . . . . . . . . . . . . . . . . 161

C.17.4 Entanglement spectrum in one-dimensional systems . . . . . . . . . . . 161

C.18 One-dimensional systems, quantum impurities and nanosystems . . 161

C.18.1 Transport out of equilbrium in the IRLM . . . . . . . . . . . . . . . . . 161

C.18.2 Friedel oscillations in the Kondo eect . . . . . . . . . . . . . . . . . . . 162

C.18.3 Eects of interactions in carbon nanotubes . . . . . . . . . . . . . . . . 162

C.18.4 Carbon nanotubes in contact with superconductors . . . . . . . . . . . . 163

C.19 Anderson localization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

C.19.1 Anderson model on Bethe lattices: density of states, localization prop-erties and isolated eigenvalue . . . . . . . . . . . . . . . . . . . . . . . . 163

C.19.2 Anderson localization transitions . . . . . . . . . . . . . . . . . . . . . . 163

C.19.3 Many body localization . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

C.19.4 Spectral features and localization properties of simple quantum systems 163

C.20 Bosonization in any dimensions and the Monte Carlo sign fermionproblem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

C.21 Open source libraries for strongly correlated systems . . . . . . . . . 164

C.22 Polymers and polyelectrolytes . . . . . . . . . . . . . . . . . . . . . . . 165

C.22.1 Block copolymer at nano-patterned surfaces . . . . . . . . . . . . . . . . 165

C.22.2 Organization of block copolymers using NanoImprint lithography: com-parison of theory and experiments . . . . . . . . . . . . . . . . . . . . . 165

C.23 Coulombic systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

C.23.1 Incorporating dipolar solvents with variable density in Poisson-Boltzmannelectrostatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

C.23.2 Solvation of ion pairs: the Poisson-Langevin model . . . . . . . . . . . . 166

C.23.3 Computing ion solvation free energies using the dipolar Poisson model . 166

C.23.4 Beyond the Poisson-Boltzmann model: modeling biomolecule-water andwater-water interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

C.24 Physics of DNA: theoretical and experimental investigations . . . . 166

C.24.1 Aggregation and adsorption at the air-water interface of bacteriophagephi X174 single-stranded DNA . . . . . . . . . . . . . . . . . . . . . . . 166

C.24.2 DNA adsorption at liquid/solid interfaces . . . . . . . . . . . . . . . . . 166

C.24.3 Mechanism of thermal renaturation and hybridization of nucleic acids:Kramers' process and universality in Watson-Crick base pairing . . . . . 167

C.24.4 A model for polymer translocation . . . . . . . . . . . . . . . . . . . . . 167

C.25 Statistical physics of homopolymeric RNA . . . . . . . . . . . . . . . 167

C.25.1 Impact of loop statistics on the thermodynamics of RNA folding . . . . 167

C.25.2 Secondary structure formation of homopolymeric single-stranded nucleicacids including force and loop entropy: implications for DNA hybridization167

C.26 Statistical physics of random RNA . . . . . . . . . . . . . . . . . . . . 168

C.26.1 Field theory for random RNA . . . . . . . . . . . . . . . . . . . . . . . . 168

C.26.2 A growth model for random RNA . . . . . . . . . . . . . . . . . . . . . 168

C.27 Pseudoknot prediction in biological RNA . . . . . . . . . . . . . . . . 169

C.27.1 Prediction of RNA secondary structures with pseudoknots . . . . . . . . 169

C.27.2 TT2NE: a novel algorithm to predict RNA secondary structures withpseudoknots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

C.27.3 Random matrix theory and RNA folding . . . . . . . . . . . . . . . . . 169

C.28 Dynamics of protein folding . . . . . . . . . . . . . . . . . . . . . . . . 169

C.28.1 Dominant reaction pathways in high dimensional systems . . . . . . . . 170


C.28.2 Kramers theory for conformational transitions of macromolecules . . . . 170

C.28.3 Stochastic dynamics and dominant protein folding pathways . . . . . . . 170

C.28.4 Simulating stochastic dynamics using large time steps . . . . . . . . . . 170

C.28.5 Dominant reaction pathways in protein folding: a direct validation againstmolecular dynamics simulations . . . . . . . . . . . . . . . . . . . . . . . 170

C.28.6 Dominant folding pathways of a peptide chain, from ab-initio quantum-mechanical simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

C.28.7 Fluctuations in the ensemble of reaction pathways . . . . . . . . . . . . 171

C.28.8 Generating transition paths by Langevin bridges . . . . . . . . . . . . . 171

C.29 Molecular motors and dynamics of actin laments . . . . . . . . . . 171

C.29.1 Molecular spiders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

C.29.2 Fluctuation relations and molecular motors . . . . . . . . . . . . . . . . 171

C.29.3 Dynamics of lament growth and instabilities . . . . . . . . . . . . . . . 172

C.30 Bioinformatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

C.30.1 Bernoulli matching model and sequence alignment . . . . . . . . . . . . 172

C.30.2 MISTRAL: a tool for energy-based multiple structural alignment of pro-teins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

C.30.3 Knotted vs. unknotted proteins: evidence of knot-promoting loops . . . 173

C.30.4 Mistral WebServer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

C.30.5 TT2NE WebServer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

Introduction

The Statistical Mechanics and Condensed Matter Theory group has a large spec-trum of activities, which are presented hereafter in three parts: Classical StatisticalPhysics, Condensed Matter Physics, and BioPhysics. The rst part is concernedwith classical systems, where quantum eects play no role (e.g. glass physics); thesecond part is devoted to quantum systems : bulk condensed matter physics (e.g.spin liquids, high-temperature superconductors or heavy fermions) and mesoscopicphysics (e.g. graphene, quantum impurities); nally, the last part is devoted to theinterface between physics and biology.

In this introduction, we rst present a very brief summary of the various activities,which are detailed in the following subsections. This section is clearly non-exhaustiveand should only be used a guide for the reader of this chapter.

Statistical physics

Out of equilibrium systems are at the core of the research on classical statisti-cal mechanics at IPhT. Indeed, while the conceptual framework for the theory ofequilibrium systems is quite well-established in statistical mechanics (with e.g. thenotion of statistical ensembles, thermodynamics, free energy), it has no equivalentfor non-equilibrium systems. As a result, even simple questions remain unanswered,e.g. how to characterize forced steady states far from equilibrium (and far fromlinear response regime) and compute their physical properties ? How to generalizethe notion of entropy or free energy in these regimes ? How to characterize the glasstransition and its slow dynamics ?

In the recent years, new uctuations theorems and relations like Jarzynski's equal-ity have started to address these issues and some works have been devoted to thisdirection (section C.1). A complementary direction of research strongly developedat IPhT consists in studying exactly solvable models of out-of-equilibrium phenom-ena, in order to explore these fundamental issues in concrete and solvable cases.


Hopefully, these models will play an analogous role to the Ising model in the elabo-ration of the theory of equilibrium phase transitions. For example, results have beenobtained in reaction-diusion models, on the asymmetric simple exclusion processmodel (ASEP), on the ABC model, or in directed Ising models, which are Isingmodels with a non conserved dynamics (section C.2).

Various aspects of stochastic processes have been studied, including the studyof the statistics of excursions (i.e. the intervals between consecutive zeros), of sev-eral stochastic processes, the maximal entropy random walk on an arbitrary graph,and new applications of stochastic Markov process to sample systems with complexenergy landscapes in Monte Carlo methods (section C.3).

In glasses, spin glasses, granular systems and some other disordered systems, therelaxation times towards equilibrium becomes so large below some critical tempera-ture that the systems never reach equilibrium and exhibits genuinely non-equilibriumphenomena, like aging. Several fundamental questions are raised with the experi-ments of various glassy systems: How to characterize the glass transition? Whatis the order parameter? Understanding these issues is an important activity in theInstitute.

In the eld of glasses, for the rst time, a qualitative thermodynamic dierencebetween the high temperature and deeply supercooled equilibrium glass formingliquid has been explicitly shown, leading to a renewed discussion of the random rstorder theory, and several other approaches, like mode coupling theory. Again, thesegeneral ideas and methods are carefully tested in several minimal solvable models,like the spiral model or kinetically constrained models, which have been studied witha combination of mathematical and numerical approaches (section C.4). Granularmedia and jamming is a related subject, studied in a fruitful collaboration withexperimentalists of the neighbouring laboratory, the Service de l'Etat Condensé(SPEC), (Cf section C.5).

Understanding the nature of the spin glass phases and of the transition fromthe high temperature disordered phase has long been a very active subject at theIPhT. Several new results have been obtained during the period of the report, e.g.on the nature of the spin glass phase in low dimensions, on the distribution ofrelaxation time in the Sherrington-Kirkpatrick model, on large random correlationsin individual mean eld sample, on the existence of a static spin glass phase on softscalar spin version of the random eld Ising model (section C.6). Besides, phasetransition and non-equilibrium dynamics of disordered systems in the presence offrozen disorder have also been studied using renormalization techniques (sectionC.7).

Finally, the tools and methods elaborated to study statistical physics systems alsohave important applications to other elds in soft condensed matter physics. Theactivity of IPhT has strongly expanded in two of these directions with the recenthirings of two permanent researchers. The rst direction is concerned with (hard)optimization problem, like e.g. the boolean satisability problem (section C.8). Thesecond direction is the study of various networks, their structure, their evolution,and more recently their spatial aspects. Networks are fundamental in theoreticalepidemiology where transportation and mobility networks are the key ingredient inthe spread of infectious diseases. The problem is then to understand the couplingbetween the movement of individuals and the spread of the disease, both processeshaving their own spatial and temporal scales. In geography and urbanism, networks


are also a key ingredient in understanding the structure and the evolution of cities(section C.9).

Condensed matter physics

In strongly correlated quantum systems, the eect of the interactions between theelectrons or the atoms deeply challenge the standard paradigms of theoretical con-densed matter physics. Standard concepts and methods, such as Fermi liquid theory,Density Functional Theory (band theory), or Landau's symmetry breaking view onphase transitions fail to account for a large number of remarkable phenomena ob-served in experiments and due to collective behaviors of fermions (or bosons). Thefractional quantum hall eect, or the high-temperature superconductivity are twofamous and spectacular examples but many other important experimental discover-ies had a major impact : metal-insulator transitions, zero-temperature continuousphase transitions in metals and magnets, breakdown of the Fermi-liquid behavior incuprates and in heavy fermions compounds, exotic orders (charge, spin, orbital) intransition metal oxides, interaction and quantum eects in low-dimensional geome-tries (articially structured nanoscale materials: dots, wires, graphene).

The research activity in condensed matter at the IPhT aims at understandingthe basic mechanisms involved in new states of matter, new phase transitions, or,more generally, new phenomena that have been (or which could be) observed in realsystems. While the study of strongly correlated materials (bulk condensed mattersystems) remain the main activity at the IPhT condensed matter theory group, newsubjects are slowly developing (e.g. graphene, eect of interaction in mesoscopicphysics, ultra-cold atoms).

Heavy fermions compounds continue to challenge the theorists with their non-Fermi liquid regime, or their quantum phase transitions. For example, the heavyfermion compound URu2Si2 and its mysterious Hidden Order phase, has receiveda renewed attention recently with new experiments. A new modulated spin liquidtheory has recently been proposed for it, in the context of a selective Mott picture ofthis class of compounds (section C.10). Besides, recent experiments on 3He bi-layersmade in the Saunders' group in London mimic the heavy fermions physics, with onelocalized layer (playing the role of the localized f electrons) and one delocalized one(playing the role of conduction electrons). These experiments have therefore beenstudied with similar theoretical tools (section C.10).

High temperature superconductivity remains a central mystery of strongly cor-related physics, in spite of the large body of available experimental data, includingseveral new recent experiments. Besides, the discovery of a new family of iron-based superconductors (the pnictides) in 2008 has driven an intense experimentaland theoretical activity. Both of these compounds have been studied at IPhT (sec-tion C.11). For the normal phase of the cuprates, a new picture of a selective Motttransition in momentum space in the Brillouin zone was proposed based on a seriesof approximate solutions of microscopic models using cluster dynamical mean eldmethods. Roughly speaking, the nodal regions remain metallic while the antinodalones become insulating, in agreement with the phenomenology. Besides, using therst implementation of dynamical mean eld theory methods within FLAPW elec-tronic structure methods, the degree of correlation of one iron-based superconductor,which was the subject of strong debates, was investigated.

Frustrated spin systems and dimer models have also been studied at IPhT (section


C.12). They are typically toy models for various materials, e.g. some insulators orthe normal phase of high-temperature superconductors in the RVB point of view.They can exhibit non-standard phases, like e.g. spin liquids, dimer phase.

The study of interaction eects in ultra-cold atomic gases of bosons and fermionshas been an emerging eld in the recent years, at the frontier of quantum opticsand condensed matter physics. These experiments have raised hope to understandfundamental issues of strongly correlated systems by creating articial solids withultra-cold atoms embedded in optical lattices, in spite of their current severe limita-tion in temperature (they are actually very hot). In the recent years, the IPhT hashad some activity in this emerging eld (section C.13): polarized superuids of theSarma type were shown to be stable at high enough interaction; a detailed discus-sion of the recent experimental realization of fermionic Mott transition in ultra-coldgases, in the ETH group in Zürich, including detailed comparison with ab-initiomicroscopic computation was provided.

Motivated by the new ultra-cold atom and mesoscopic experiments, the out-of-equilibrium dynamics of quantum open or closed systems have been a subject ofrenewed interest. Several works have been devoted to this issue (cf section C.16).

Mesoscopic systems and nanosystems constitute another direction of research atIPhT. Quantum impurity models, out of equilibrium transport and various aspectsof nanotubes have been studied (section C.18). Graphene has received a lot ofattention recently, due e.g. to the Dirac character of its low-energy excitations.Still, many important questions concerning the eects of disorder, of the substrateand of interactions remain unanswered. Several works have been devoted to thesequestions by C. Bena (regular visitor from Orsay), using the spatial variations oflocal density of states in order to establish both the nature of disorder in graphene,to retrieve information about the chirality of the quasiparticles and the form of thequasiparticle wavefunction; some of these predictions have been conrmed by recentscanning tunneling microscopy experiments.

Various aspects of the Anderson localisation problem have been studied (sectionC.19), including in the many-body case using e.g. exact renormalization methods.

Finally, most of the condensed matter systems studied at IPhT are in strong cor-relation regime, in which perturbative or conventional mean-eld calculations arewell known to be inappropriate. More elaborate theoretical tools or ideas need tobe employed or developed to tackle these problems: (conformal) eld theory, renor-malization group, new approximation technique or innovative algorithms. At IPhT,a strong eort is devoted to these methodological developments. For example, anew bosonization technique in dimension greater than one was proposed (cf sectionC.20), which may also provide a new perspective on the (in)famous sign problemof Quantum Monte Carlo algorithms; an ecient algorithm for solving multiplequantum impurity models and (cluster) dynamical mean eld methods has beendeveloped and is now routinely used in several groups worldwide (cf section C.11);quantum entanglement properties have been studied in various systems (sectionC.17), inspiring new ways to probe the nature of the many-body wave functions ofcritical one-dimensional systems, e.g. spin chains; some connection with 2d quantumsystems have also be explored (section C.17); the use of integrability to computephysical quantities (e.g. current) in out-of-equilibrium steady states has been care-fully investigated in some model systems (cf section C.18).


Biophysics

Soft Condensed Matter, Biological Systems and Interdisciplinary Physics is slowlydeveloping at IPhT. The group has enlarged its spectrum beyond that of biopolymersand electrostatics in biological systems to include molecular motors, epidemiology,spatial networks, etc. In addition, the group has started to deal with questions ofdirect interest to real biological systems and is providing WebServers for proteinstructure alignment and for RNA pseudoknot predictions.

Biophysics as it is done at the IPhT, is at the crossroads of Soft CondensedMatter theory , Disordered Systems and non-equilibrium Statistical Physics.

Soft Matter theory enters biophysics through polymer theory, in the study ofbiopolymers, their melting transitions, their response to external forces, etc. , andthrough Coulombic systems, in the study of the solvation of proteins, of the waterand ions distribution, etc.

Biopolymers such as DNA, RNA and proteins, have a chemical sequence de-pendence which can be modeled, to a rst approximation, as a quenched randomsequence. In addition to the melting transition, random RNA undergoes a freezingtransition, of the same type as those studied in Disordered Systems.

Finally, molecular motors, the dynamics of actin laments, and also the kineticsof protein folding all involve the use of methods and concepts of non-equilibriumStatistical Physics.

One of the main characteristics of this group is the utilization of the most so-phisticated techniques of statistical physics, such as eld theory, matrix eld theory,path integrals, the Bethe Ansatz, stochastic equations, etc.. In addition to thesesophisticated analytic works, elaborate numerical calculations are also performedin order to determine folding pathways of proteins or to predict RNA secondarystructures.

Finally, two WebServers have been set up. One, entitled Mistral, allows multiplestructure alignment of protein structures. By aligning protein structures, one canlook for structurally conserved motifs in proteins, and this in turn can be used todetermine the function of proteins or their evolution. The other server, TT2NE, pre-dicts secondary structures of RNA with pseudoknots, from their chemical sequence.This is an important information, since loops and pseudoknots are known to embedthe binding sites of RNA.


C.1 Fluctuation theorems and re-lated identities

C.1.1 Fluctuation theorems and workidentities (K. Mallick)

During the last decade, many exact relationsfor non-equilibrium processes have been derived.The Jarzynski equality is one of these remark-able results. This relation implies that the sta-tistical properties of the work performed on asystem in contact with a heat reservoir at con-stant temperature during a non-equilibrium pro-cess are related to the free energy dierence be-tween two equilibrium states of that system.

In [t10/217], we study non-equilibrium workrelations for a space-dependent eld with sto-chastic dynamics (Model A). Jarzynski's equal-ity is obtained through symmetries of the dy-namical action in the path integral represen-tation. We derive a set of exact identitiesthat generalize the uctuation-dissipation rela-tions to non-stationary and far-from-equilibriumsituations and argue that these identities areprone to experimental verication. Further-more, we show that a well-studied invarianceof the Langevin equation under supersymmetry,which is known to be broken when the externalpotential is time-dependent, can be partially re-stored by adding to the action a term which isprecisely Jarzynski's work. The work identitiescan then be retrieved as consequences of the as-sociated Ward-Takahashi identities.

In [t11/012], we prove a generalizeductuation-dissipation relation that is valid fora system perturbed in the vicinity of a non-equilibrium steady-state and obeying a discreteMarkov dynamics. We derive this relation usinga generalized form of the Sasa relation (whichis an extension of Jarzynski's identity to non-equilibrium states) that we derive by studyingthe time-reversed Markov chain. We explainhow this generalized uctuation-dissipation re-lation can be understood in terms of trajectoryentropy excess. The results are illustrated on asimple pedagogical example of a molecular mo-tor.

In [t09/255], we derive Fluctuation Rela-tions for quantum Markovian dynamical sys-tems. Many works on quantum uctuation re-lations, including the pioneering ones, consideronly closed systems (i.e. unitary evolution) pre-pared in a Gibbs state and isolated from theirenvironment during their evolution which is thusunitary. In our work, we use the Lindblad mas-ter equation which is an eective model for anon-equilibrium open quantum system, widely

used in Quantum Optics. The Lindbladian evo-lution is a non-unitary dynamics for the den-sity matrix of the open system. By investi-gating the general properties of the Lindbladequation under time-reversal, we prove a quan-tum analog of Jarzynski's relation. Besides, weshow that, in the vicinity of a quantum non-equilibrium steady state, this identity impliesa generalized quantum uctuation-dissipationtheorem. Then, we prove a generic relationamongst correlation functions, a kind of book-keeping formula which yields the quantum ana-log of Crooks' relations. In the special case ofconservative Hamiltonian dynamics (closed sys-tem), the relations we obtain are identical topreviously known quantum work theorems. Inparticular, we show that for a closed system,the generalized uctuation-dissipation theoremreduces to the celebrated Callen-Welton-Kuboformula.

Recent developments in Non-EquilibriumStatistical Mechanics with emphasis on the workidentities and on the Gallavotti-Cohen sym-metry in Markovian systems were reviewed in[t09/322]. A series of lectures on this topic wasalso given at the IPhT, in May-June 2009. Thelecture notes are available at [t09/249].

C.1.2 Maximization of the Shannon en-tropy of dynamical trajectories (C.Monthus)

In [t11/050], we discuss the simplest general-ization of statistical physics to non-equilibriumsteady states: the principle is to maximize theShannon entropy associated with the probabil-ity distribution of dynamical trajectories in thepresence of constraints, including the macro-scopic current of interest, via the method ofLagrange multipliers. This approach yieldsGibbs distribution for dynamical trajectories,and the Gallavotti-Cohen symmetry is automat-ically satised.

C.1.3 A meaningful expansion arounddetailed balance (B. Wynants)

In [t11/042], we consider Markovian dynamicsmodeling open mesoscopic systems which aredriven away from detailed balance by a noncon-servative force. A systematic expansion is ob-tained of the stationary distribution around anequilibrium reference, in orders of the nonequi-librium forcing. The rst order around equilib-rium has been known since the work of McLen-nan (1959), and involves the transient irre-versible entropy ux. The expansion generalizesthe McLennan formula to higher orders, com-









plementing the entropy ux with the dynamicalactivity. In that way nonlinear response aroundequilibrium can be meaningfully discussed interms of two main quantities only, the entropyux and the dynamical activity. The expansionmakes mathematical sense as shown in the sim-plest cases from exponential ergodicity.

C.1.4 The modied SutherlandEinsteinrelation for diusive nonequilibria(B. Wynants)

There remains a useful relation between diu-sion and mobility for a Langevin particle in a pe-riodic medium subject to nonconservative forces.The usual uctuation-dissipation relation eas-ily gets modied and the mobility matrix is nolonger proportional to the diusion matrix, witha correction term depending explicitly on the(nonequilibrium) forces. In [t11/043], we dis-cuss this correction by considering various sim-ple examples and we visualize the various depen-dencies on the applied forcing and on the timeby means of simulations. For example, in allcases the diusion depends on the external forc-ing more strongly than does the mobility. Wealso give an explicit decomposition of the sym-metrized mobility matrix as the dierence be-tween two positive matrices, one involving thediusion matrix, the other forceforce correla-tions.

C.1.5 Monotone return to steadynonequilibrium (B. Wynants)

In [t11/154], we propose and analyze a new can-didate Lyapunov function for relaxation towardsgeneral nonequilibrium steady states. The pro-posed functional is obtained from the large timeasymptotics of time-symmetric uctuations. Fordriven Markov jump or diusion processes itmeasures an excess in dynamical activity rates.We present numerical evidence and we report ona rigorous argument for its monotonous time-dependence close to the steady nonequilibriumor in general after a long enough time. Thisis in contrast with the behavior of approximateLyapunov functions based on entropy produc-tion that when driven far from equilibrium oftenkeep exhibiting temporal oscillations even closeto stationarity.

C.2 Exactly solvable models out ofequilibrium

C.2.1 Some exactly solvable models outof equilibrium (K. Mallick)

Statistical physics of systems far from equi-librium does not have yet denite theoreti-

cal foundations. Universal properties of non-equilibrium statistical physics are successfullyexplored through the investigation of stochasticprocesses, that are governed by simple dynami-cal rules at the microscopic level but that displaya rich macroscopic behavior.

The ballistic aggregation model is one of thesimplest interacting particles processes of non-equilibrium statistical mechanics and as suchhas attracted a lot of attention in the pastdecades. It represents a sticky gas of N par-ticles with random initial positions and veloci-ties, moving deterministically, and forming ag-gregates when they collide. In [t08/209], weinvestigate the long time behavior of the one-dimensional ballistic aggregation model and ob-tain a closed formula for the stationary measureof the system. In particular, we identify uni-versal properties which are independent of theinitial position and velocity distributions of theparticles, study cluster distributions and deriveexact results for extreme value statistics (be-cause of correlations these distributions do notbelong to the Gumbel-Fréchet-Weibull univer-sality classes). This model generates dynami-cally many dierent scales and can be viewedas one of the simplest exactly solvable model ofN -body dissipative dynamics

In [t09/157], we consider a non-equilibriumreaction-diusion model on a nite one dimen-sional lattice with bulk and boundary dynam-ics inspired by Glauber dynamics of the Isingmodel. We show that the model has a rich alge-braic structure that we use to calculate its prop-erties. In particular, we show that the Markovdynamics for a system of a given size can beembedded in the dynamics of systems of highersizes. This remark leads us to devise a tech-nique we call the transfer matrix Ansatz thatallows us to determine the steady state distribu-tion and correlation functions. Furthermore, weshow that the disorder variables satisfy very sim-ple properties and we give a conjecture for thecharacteristic polynomial of Markov matrices.Lastly, we compare the transfer matrix Ansatzused here with the matrix product representa-tion of the steady state of one-dimensional sto-chastic models. In [t09/252], we prove that thetransfer matrix Ansatz method also applies tothe simple exclusion process with open bound-aries.

In the eld of non-equilibrium statisticalmechanics, the Asymmetric Simple ExclusionProcess (ASEP) has reached the status of aparadigm. The ASEP is a discrete lattice-gasmodel of interacting particles in which particles







hop while satisfy an exclusion constraint. A nat-ural generalization of the ASEP is to considermodels with dierent types (or colors) of par-ticles. Such systems, called multispecies asym-metric exclusion process, arise naturally in thestudies of shocks or by applying the couplingtechnique in probability theory. The descriptionof the steady-state of such models was a long-standing open problem that we have studied ina series of papers. In [t08/134], we constructthe stationary measure of the N species totallyasymmetric exclusion process in a matrix prod-uct formulation; we make the connection be-tween the matrix product formulation and queu-ing theory: this allows us to interpret the op-erators that appear in the Matrix Ansatz asmatrices acting on the (innite) space of queuelengths. In [t08/213], we generalize the matrixapproach to the Partially asymmetric process forwhich no mapping to queuing theory was avail-able: the matrix Ansatz is found by taking ten-sor products of quadratic algebras and we give apurely algebraic proof of the stationarity of theinvariant measure. Besides, the matrix algebrais re-interpreted in terms of the action of a trans-fer matrix Finally, in [t11/046], we construct ageneral transfer matrix Ansatz between multi-species exclusion processes with dierent num-bers of species and analyze recursive combina-torial structures within the set of these dierentmodels, which can be encoded in a Hasse dia-gram. We prove that the Matrix Ansatz is infact a mapping that intertwines Markov Matri-ces of dierent stochastic systems and this allowsus to construct non only the stationary state butalso full sectors of the spectrum i.e., relaxationstates.

C.2.2 Large deviations of the current inthe exclusion process (K. Mallick)

An important physical quantity in the ASEPis the statistics of the current in the station-ary regime (this current corresponds to a localheight variable in the corresponding random in-terface model). In particular, large deviations,that are expected to play an essential role in non-equilibrium statistical physics, are a very rele-vant quantity to measure, to compute numeri-cally and, if possible, to calculate analytically.

For the exclusion process on a periodic ring,the large deviation function of the current wasdetermined by Derrida and Lebowitz in 1999,but only for the particular case of the totallyasymmetric exclusion process (TASEP). Thisresult was derived using the Bethe equationswhich, for the TASEP, can be solved explicitly

thanks to a decoupling property that reducesthem to a one variable polynomial equation plusa self-consistency condition. In the general case,when jumps on both directions are allowed, theBethe equations do not decouple and the prob-lem remained unsolved for almost ten years. Thegeneral case is important to understand hownon-equilibrium behavior builds itself up start-ing from the equilibrium (i.e. detailed-balance)case. In [t07/181], we overcame this technicalbarrier by using a functional reformulation ofthe Bethe Ansatz that maps it into a purely alge-braic problem of polynomial factorization: thisallowed us to calculate the rst two cumulantsof the current (K. Mallick and S. Prolhac).

In [t08/236], we studied the weakly asym-metric limit and obtained the complete largedeviation function at dominant order w.r.t. tothe size of the system. Previously, T. Bodineauand B. Derrida used the continuous (hydrody-namic) limit of model and applied Jona-Lasinio'smacroscopic uctuation theory; they predicted anon-equilibrium phase transition with respect toa fugacity parameter, conjugate to the currentvariable. The exact calculation of [t08/236] con-rms the existence of this transition, which cor-responds to a breaking of analyticity in the largedeviation function, emphasizing again the im-portance of this observable in systems far fromequilibrium (K. Mallick and S. Prolhac).

In [t08/198], Sylvain Prolhac was able to de-termine the expression of the third order cu-mulant (skewness) for an arbitrary value of theasymmetry parameter. The skewness measuresthe non-Gaussian character of the probabilitydistribution and its non-vanishing is a sign ofthe non-equilibrium character of the statistics.Finally, the complete problem of the current'sstatistics in the exclusion process on a ring wasentirely solved by S. Prolhac in [t10/106]. There,a combinatorial expression for all the cumulantsin all the cases was derived. In the thermody-namic limit, three dierent scaling regimes canbe observed for the current uctuations, depend-ing on how the asymmetry scales with the sizeL of the system: the Edwards-Wilkinson phase,the Kardar-Parisi-Zhang universality class, andan intermediate regime (with asymmetry 1/Land 1/

√L) for which no large scale continu-

ous description is yet known.These recent results on the exclusion pro-

cess have been reviewed in the STAPHYS Pro-ceedings [t11/096] and in the Lecture Notes[t10/064].

The analytical study of the uctuations ofthe current uctuations in the original totally












asymmetric exclusion process (TASEP) on a -nite one-dimensional lattice with open bound-aries (i.e., in contact with two reservoirs at dif-ferent potentials) is a very challenging problem.This question naturally arose in this eld at thetime when the rst exact solutions of the ASEPwere found but it has remained unsolved andvexing since then. This is far from being a purelyacademic problem: it is important because inpresence of reservoirs, the ASEP model becomesa rather realistic description of 1d transport andit can be related to real experimental situations(quantum dots). Only the mean value and thevariance of the current had been calculated inthe beginning of the 90's. In the weakly asym-metric regime, progress was made using a macro-scopic additivity principle. In [t11/096], we havefound a formula for the generating function ofthe cumulants of the current in the open TASEP,which is related to the large deviation functionby Laplace transform. This formula is of combi-natorial nature and it is valid for all system sizesand for all values of the chemical potentials ofthe reservoir. All previously known cases are re-trieved as special limits and the behavior of thelarge deviation function in the phase diagramcan be precisely analyzed (A. Lazarescu and K.Mallick).

C.2.3 Algebraic properties of a disor-dered asymmetric Glauber model(A. Ayyer)

In [t11/108] we study a system of spins on a -nite one-dimensional lattice, with one open andone closed boundary. The dynamical rules arechosen to be an asymmetric version of Glauberdynamics. For this model, we prove an ex-plicit formula for the characteristic polynomialof the transition matrix of the associated Markovchain. We also analyzed two special cases of themodel, which resemble a ferromagnetic and an-tiferromagnetic Ising chains.

C.2.4 On some classes of open two-species exclusion processes (A.Ayyer)

In [t10/133] (with J. L. Lebowitz and E. R.Speer) we consider a totally asymmetric exclu-sion process with two species on a nite one-dimensional lattice with open boundaries. Thismodel generalizes previous work in which secondclass particles can neither enter nor leave the sys-tem. For certain classes of rates we compute thecurrents and phase diagram, and in some otherclasses, we obtain some monotonicity properties.We also analyze a simple example where there is

a shock in which the densities of all three speciesare discontinuous.

C.2.5 The spectrum of an asymmetricannihilation process (A. Ayyer)

In an earlier work with Kirone Mallick [t09/157]on the asymmetric annihilation process, we hadconjectured an explicit formula for the charac-teristic polynomial of the transition matrix ofthe associated Markov chain. In [t10/100] (withVolker Strehl), we prove that conjecture by gen-eralizing the model using the Hadamard trans-form (a kind of discrete Fourier transform).

C.2.6 Phase diagram of the ABC modelon an interval (A. Ayyer)

The three species asymmetric ABC model wasinitially dened on a ring by Evans, Kafri, Ko-duvely, and Mukamel, and the weakly asymmet-ric version was later studied by Clincy, Derrida,and Evans. In [t09/070] (with E. A. Carlen, J.L. Lebowitz P. K. Mohanty D. Mukamel andE.R. Speer) the latter model is studied on a one-dimensional lattice of N sites with closed (zeroux) boundaries. In this geometry the local par-ticle conserving dynamics satises detailed bal-ance with respect to a canonical Gibbs mea-sure with long range asymmetric pair interac-tions. This generalizes results for the ring case,where detailed balance holds, and in fact thesteady state measure is known only for the caseof equal densities of the dierent species: in thelatter case the stationary states of the systemon a ring and on an interval are the same. Weprove that in the N to innity limit the scaleddensity proles are given by (pieces of) the peri-odic trajectory of a particle moving in a quarticconning potential. We further prove unique-ness of the proles, i.e., the existence of a sin-gle phase, in all regions of the parameter space(of average densities and temperature) except atlow temperature with all densities equal; in thiscase a continuum of phases, diering by transla-tion, coexist. The results for the equal densitycase apply also to the system on the ring, andthere extend results of Clincy et al.

C.2.7 Non equilibrium stationary statesand phase transitions in directedIsing models (C. Godrèche)

The studies of the Katz-Lebowitz-Spohn model,of the Simple Exclusion Process, or of the ZeroRange Process, among others, showed that im-posing a bias on a reversible stochastic pro-cess leading to equilibrium changes its proper-ties drastically. The process, which is no longerreversible, reaches a stationary state in the long-








time regime, whose description is far more di-cult than its equilibrium counterpart.

A similar question can be posed for the ki-netic Ising model with non conserved dynamics.The idea is that each spin is inuenced by onlya subset of its nearest neighbors and thereforethe asymmetry of the dynamics violates the re-versibility of the process. We shall name thesemodels directed Ising models. The questionsposed are: what are the consequences of impos-ing a bias on the model? Are the dynamicalproperties changed? Is the stationary state of adierent nature? The two papers [t09/309] and[t11/098], are devoted to these questions.

In the rst one, [t09/309], the nonequilib-rium properties of directed Ising models withnon-conserved dynamics, in which each spinis inuenced by only a subset of its nearestneighbors, is studied. We treat the followingmodels: (i) the one-dimensional chain; (ii) thetwo-dimensional square lattice; (iii) the two-dimensional triangular lattice and (iv) the three-dimensional cubic lattice.

We raise and answer the question: (a) underwhat conditions is the stationary state describedby the equilibrium Boltzmann-Gibbs distribu-tion? We show that, for models (i), (ii) and (iii),in which each spin sees only half of its neigh-bors, there is a unique set of transition rates,namely with exponential dependence in the localeld, for which this is the case. For model (iv),we nd that any rates satisfying the constraintsrequired for the stationary measure to be Gibb-sian should satisfy detailed balance, ruling outthe possibility of directed dynamics. We nallyshow that directed models on lattices of coordi-nation number z ≥ 8 with exponential rates can-not accommodate a Gibbsian stationary state.We conjecture that this property extends to anyform of the rates. We are thus led to the con-clusion that directed models with Gibbsian sta-tionary states only exist in dimensions one andtwo.

We then raise the question: (b) do directedIsing models, augmented by Glauber dynam-ics, exhibit a phase transition to a ferromag-netic state? For the models considered above,the answers are open problems, with the excep-tion of the simple cases (i) and (ii). For Cayleytrees, where each spin sees only the spins fur-ther from the root, we show that there is a phasetransition provided the branching ratio, q, sat-ises q ≥ 3. In the second one [t11/098], thestudy by Glauber of the time-dependent statis-tics of the Ising chain is extended to the casewhere each spin is inuenced unequally by its

nearest neighbors. The asymmetry of the dy-namics implies the failure of the detailed bal-ance condition. The functional form of the rateat which an individual spin changes its state isconstrained by the global balance condition withrespect to the equilibrium measure of the Isingchain. The local magnetization, the equal timeand two-time correlation functions and the lin-ear response to an external magnetic eld obeylinear equations which are solved explicitly. Thebehavior of these quantities and the relation be-tween the correlation and response functions areanalyzed both in the stationary state and in thezero-temperature scaling regime. In the station-ary state, a transition between two behaviors ofthe correlation function occurs when the ampli-tude of the asymmetry crosses a critical value,with the consequence that the limit uctuation-dissipation ratio decays continuously from thevalue 1, for the equilibrium state in the absenceof asymmetry, to 0 for this critical value. At zerotemperature, under asymmetric dynamics, thesystem loses its critical character, yet keepingmany of the characteristic features of a coarsen-ing system.

C.3 Stochastic processes

C.3.1 Longest excursion of stochasticprocesses in nonequilibrium sys-tems (C. Godrèche)

In [t09/310], we consider the excursions, i.e., theintervals between consecutive zeros, of stochasticprocesses that arise in a variety of nonequilib-rium systems and study the temporal growth ofthe longest one lmax(t) up to time t. For smoothprocesses, we nd a universal linear growth <lmax(t) >∼ Qt with a model dependent ampli-tude Q. In contrast, for non smooth processeswith a persistence exponent theta, we show that< lmax(t) > has a linear growth if θ < θc while< lmax(t) >∼ t1−ψ if θ > θc. The ampli-tude Q and the exponent θc are novel quanti-ties associated with nonequilibrium dynamics.This behavior is obtained by exact analyticalcalculations for renewal and multiplicative pro-cesses and numerical simulations for other sys-tems such as the Ising model under coarseningdynamics as well as the diusion equation withrandom initial conditions.

C.3.2 Random walk and related sto-chastic processes (J.M. Luck)

We have introduced maximal entropy randomwalk (MERW) on an arbitrary graph. Our ini-tial motivation was to provide a faithful dis-cretization of the Feynman path integral, where







Figure C.1: Space-time representation of the zero-temperature biased coarsening of the directedIsing chain with periodic boundary conditions

all paths of given length and endpoints would beequally probable. MERW can be alternativelydened as the discrete-time random walk whichmaximizes the entropy production rate. Its con-struction is germane to that of Shannon-Parrymeasures known in ergodic theory. The corre-sponding hopping probabilities are determinedby the Perron-Frobenius eigenvalue and eigen-vector of the adjacency matrix of the graph.MERW coincides with Pólya's usual randomwalk on graphs where all the nodes have thesame degree. It may however exhibit unexpectedlocalization features. In the case of a regularlattice with a weak bond dilution, the station-ary probability of nding a particle performingMERW localizes in the largest nearly sphericalLifshitz region of the lattice which is free ofdefects [t08/165, t10/051].

An imaginary exponential functional ofBrownian motion has been scrutinized. Thisrandom complex integral shows up naturallyas a tool in the study of the binary annihi-lation process, within the Doi-Peliti formalismfor reaction-diusion systems, once every spa-tial dependence has been neglected. The mainemphasis has been put on the complementar-ity between the usual Langevin approach andanother approach based on the similitude withKesten variables and one-dimensional disorderedsystems [t11/005].

C.3.3 Do solids ow? (G. Biroli)

In collaboration with J. Kurchan and F. Saus-set [t10/110], we showed that solidity is only atime-scale dependent notion: equilibrium statesof matter that break spontaneously translation

invariance, e.g. crystals, ow if even an innites-imal stress is applied. However, they do so ina way inherently dierent from ordinary liquidssince their viscosity diverges for vanishing shearstress with an essential singularity. We found anultra-slow decrease of the shear stress as a func-tion of the shear rate, which explains the ap-parent yield stress identied in rheological owcurves. Finally, we suggested that an alternat-ing shear of frequency ω and amplitude γ shouldlead to a dynamic phase transition line in the(ω,γ) plane, from a owing to a non-owingphase.

C.3.4 Slow annealing through criticalpoints: the Kibble-Zurek mecha-nism revisited (G. Biroli)

In collaboration with L. Cugliandolo and A. Si-cilia [t10/109], we revisited the Kibble-Zurekmechanism introduced to explain the dynamicsof phase ordering systems during an innitelyslow annealing across a second order phase tran-sition. We elucidated the time and cooling ratedependence of the typical growing length and weused it to predict the number of topological de-fects left over in the symmetry broken phase asa function of time, both close and far from thecritical region. Our results extend the Kibble-Zurek mechanism and reveal its limitations.

C.3.5 First passage in innite parabo-loidal domains (P. Krapivsky)

First passage and diusion problems naturallyappear in numerous phenomena in physics,chemistry and biology. In many models, oneconsiders a particle conned in a domain and







absorbed whenever it hits the boundaries. Thesurvival probability of such a particle is a func-tion of the conning domain. A particle en-closed in a nite volume will decay exponen-tially. When the domain is innite, more in-teresting algebraic decay can occur, dependingon the geometric properties of the enclosure. In[t10/194], Paul Krapivsky and Sid Redner inves-tigate the rst passage problem in generalizedparaboloidal domains, of arbitrary dimension,dened by the equation y = a(x2

1+. . .+x2d−1)p/2

where p > 1. By using an extreme statisticsargument (also known as a Lifshitz tail argu-ment), the authors show that when a particle isinside the paraboloid, its survival property S(t)generically decays as a stretched exponential,lnS ∼ −t(p−1)/(p+1), independent of the spa-tial dimension. This also allows them to deter-mine the average hitting time. However, whenthe particle is outside the paraboloid and is ab-sorbed when hitting it, dimensionality mattersbut the exponent p characterizing the paraboloidis irrelevant: For d = 2, we have S(t) ∼ t−1/4

and for d = 3, S(t) ∼ (ln t)−1. In higher di-mensions, the particle survives with nite prob-ability. The authors also investigate the situa-tion where the interior of the paraboloid is ini-tially uniformly lled with non-interacting dif-fusing particles that are absorbed by the bound-ary and calculate the time dependence of the dis-tance between the apex and the particle closestto the apex. These studies shed a new light onthe interplay between diusion processes, rstpassage times and geometry.

C.3.6 Zero-temperature dynamics inthe 3d Ising-Glauber model (P.Krapivsky)

The aim of studies in coarsening dynamics is tounderstand how ordered phases that are thermo-dynamically favored below the critical tempera-ture in systems with short-ranged interactionscan be formed dynamically. An archetypal ex-ample is the Ising model endowed with Glauberdynamics, where domains consist of spins thatall point up or point down. When such an Isingmodel, initially in the high temperature phase, isquenched at the nal temperature T = 0, energyraising spin ips are forbidden. In that case,the possibility exists that the model falls intoa local minimum, i.e., a state whose energy islower than any other state that diers by onespin-ip. At zero temperature, the system maynot be able to escape from such a local mini-mum state and thus will never reach the trueground state. A one dimensional system of -

nite size L ultimately reaches complete align-ment -the ground state. In two dimensions, theground state is reached with probability p < 1(p is roughly 2/3) and with probability 1 − pthe system may end up in a state that con-sists of an even number of straight strips. Ingreater than two dimensions, the probability ofreaching the ground state decays very rapidlywith L (the typical size of the system) and, inpractice, the ground state is never reached. In[t10/192], P. Krapivsky et al. consider the caseof the 3d Glauber-Ising model on a periodiccubic lattice and show that typical metastablestates can be viewed as the discrete analogs ofminimal surfaces. Such long-time states are notstatic and do not consist in isolated congura-tions. Rather, they form a connected iso-energyset within which the system wanders forever byipping `blinker' spins ad innitum with no en-ergy cost. The authors investigate the topol-ogy of a typical metastable domain and ndthat its genus g grows algebraically with sys-tem size: 〈g〉 ∼ Lγ with γ ∼ 1.7. Because of theblinker states, the energy relaxation is extremelyslow, with characteristic time that grows expo-nentially with system size.

C.3.7 A light impurity in an equilibriumgas (P. Krapivsky)

In [t10/193], P. Krapivsky and L. D'Alessio in-vestigate the evolution of a light impurity parti-cle in a Lorentz gas where the background atomsare in thermal equilibrium. This problem, rem-iniscent of Fermi's model for cosmic rays accel-eration, is a natural generalization of the stan-dard Lorentz gas is which scatters are assumedto be immobile. The behavior of the light par-ticle is analyzed using the Boltzmann equationframework. The authors show that in the longtime limit, the collision term of the Boltzmannequation simplies allowing them to reduce theintegro-dierential Lorentz-Boltzmann equationto a partial dierential equation. By studyingthe resulting equation, the authors calculate theaverage particle displacement and show that itgrows linearly with time and proportionally tothe thermal velocity of the background atoms-the density of the gas, the size of atoms andthe details of the interaction between the par-ticle and the atoms do not aect the asymp-totic. The thermal motion of the backgroundatoms causes the average particle speed to growas tλ/(2(d−1)+λ) where λ characterizes the diver-gence of interaction potential at short distancesr (the interaction behaves as r−λ) and d is the di-mension. The authors also calculate the univer-





sal scaling laws for the velocity and position dis-tributions. Generically, these distributions arenot Gaussian. The theoretical predictions are inperfect agreement with numerical simulations.

C.3.8 Accelerated sampling of Boltz-mann distributions (H. Orland)

The sampling of Boltzmann distributions by sto-chastic Markov processes, can be strongly lim-ited by the crossing time of high (free) energybarriers. As a result, the system may staytrapped in metastable states, and the relaxationtime to the equilibrium Boltzmann distributionmay be very large compared to the availablecomputational time. In [t08/285], we show how,by a simple modication of the Hamiltonian, onecan dramatically decrease the relaxation time ofthe system, while retaining the same equilibriumdistribution. The idea is to decrease the relax-ation time to equilibrium by increasing the gapof the Hamiltonian.This is done by adding to theHamiltonian a term proportional to the projec-tor to its ground state. The method is illustratedon the case of the one-dimensional double-wellpotential.

C.3.9 Accelerated stochastic sampling ofdiscrete statistical systems (H. Or-land)

We propose in [t10/260] a method to reducethe relaxation time towards equilibrium in sto-chastic sampling of complex energy landscapesin statistical systems with discrete degrees offreedom by generalizing the platform previouslydeveloped for continuous systems. The methodstarts from a master equation. The masterequation is transformed into an imaginary-timeSchrödinger equation. The Hamiltonian of theSchrödinger equation is modied by adding aprojector to its known ground state. We showhow this transformation decreases the relaxationtime and propose a way to use it to acceleratesimulated annealing for optimization problems.We implement our method in a simplied kineticMonte Carlo scheme and show an accelerationby an order of magnitude in simulated anneal-ing of the symmetric traveling salesman prob-lem. Comparisons of simulated annealing aremade with the exchange Monte Carlo algorithmfor the three-dimensional Ising spin glass. Ourimplementation can be seen as a step towardaccelerating the stochastic sampling of genericsystems with complex landscapes and long equi-libration times.

C.4 Glass physics

C.4.1 A theoretical perspective on theglass transition and nonequilib-rium phenomena in disorderedmaterials (G. Biroli)

In collaboration with L. Berthier we wrote areview, to be published on Review of ModernPhysics, [t10/273] that provides a theoreticalperspective on the glass transition in molecularliquids at thermal equilibrium, on the spatiallyheterogeneous and aging dynamics of disorderedmaterials, and on the rheology of soft glassy ma-terials.

C.4.2 Dynamical heterogeneity inglasses, colloids and granular ma-terials (G. Biroli)

In collaboration with L. Berthier, J.-P. Bou-chaud, L. Cipelletti, W. van Saarloos we editeda book [t11/106] on dynamical heterogeneitythat will be published in July 2011 by OxfordUniversity Press. It provides a broad and up-to-date overview of the current understandingof dynamic heterogeneity in glasses, colloids,and granular media. The book contains formalchapters about recent theoretical developmentsand very phenomenological ones concerned withmore practical and experimental aspects. Sucha broad scope would have been dicult to coverby a single author. We have therefore mustereddierent scientists, who have all made impor-tant contributions to the eld. In collaborationwith L. Berthier, J.-P. Bouchaud and R. Jack wewrote a chapter [t10/268] of the book in whichwe review the recent progress and the open ques-tions about the characterization of dynamic het-erogeneity in glassy materials.

C.4.3 Lattice models and the glass tran-sition (G. Biroli)

In order to gain a deeper understanding of theglass transition we have studied several latticemodels. In collaboration with C. Toninelli, werigorously proved in [t07/128] that the spiralmodel has an ideal glass phase transition andobtained the corresponding critical properties,thus conrming the previous results obtainedwith D.S. Fisher. In collaboration with F. Saus-set, G. Tarjus and C. Toninelli [t09/227] westudied Kinetically constrained models (KCMs)on hyperbolic lattices obtained by regular tilingsof the hyperbolic plane. We showed that forgeneric tilings there exists a dynamical glasstransition, which has a mixed character: it isdiscontinuous but characterized by a divergingcorrelation length, similarly to what happens on









Bethe lattices and random graphs of constantconnectivity. In collaboration with R. Darst andD. Reichman, we introduced [t09/225] a new lat-tice glass model whose dynamical rules are basedon thermodynamic considerations, as opposed tothe purely kinetic ones of KCMs. We showed bynumerical simulations that it is a qualitativelygood model of glass-formers, in particular it dis-plays violations of the Stokes-Einstein relationand the growth of various length scales associ-ated with dynamical heterogeneity.

C.4.4 Theory of the glass transition:random rst order transition (G.Biroli)

In collaboration with J.-P. Bouchaud et al. weshowed [t08/151] for the rst time a qualita-tive thermodynamic dierence between the hightemperature and deeply supercooled equilibriumglass-forming liquid: the inuence of boundaryconditions propagates into the bulk over largerand larger length scales upon cooling. The in-crease of this length scale is a clear signature ofthe emergence of some hidden static order, as itwas expected within the random rst-order tran-sition theory (RFOT) of the glass transition. Incollaboration with J.-P. Bouchaud, we reviewedthe RFOT picture for glasses [t09/239]: the ba-sic arguments and the intuition bolstering thetheory, the pros and cons that support or un-dermine it, the directions, both theoretical andexperimental, where progress is needed to ascer-tain the status of RFOT. Finally, we comparedRFOT to other recent theories, including elasticmodels, Frustration Limited Domains or Kinet-ically Constrained models. Recently, in collab-oration with C. Cammarota, G. Tarjus and M.Tarzia, we developed [t10/121] the rst renor-malization group (RG) analysis of RFOT. Weused a Migdal-Kadano real space method ap-plied directly on the replica eld theory. Withinthis approximation we found that along the RGow the properties associated with metastableglassy states, such as the congurational en-tropy, are only dened up to a characteristiclength scale that diverges as one approaches theideal glass transition. The critical exponentscharacterizing the vicinity of the transition arethe usual ones associated with a rst-order dis-continuity xed point.

C.4.5 Theory of the glass transition:mode coupling theory (G. Biroli)

In collaboration with A. Billoire, J.-P. Bouchaudand T. Sarlat, we studied numerically a dis-ordered spin model, the fully connected Ran-

dom Orthogonal Model, for which the predic-tions of the Mode Coupling Theory (MCT) ofthe glass transition hold exactly. Our conclu-sion [t09/094] is that the quantitative predic-tions of MCT are exceedingly dicult to testeven for models for which MCT is exact becauseof strong pre-asymptotic eects. Furthermore,we found that naive nite size scaling is vio-lated at the MCT transition. In collaborationwith A. Andreanov and J.-P. Bouchaud, we de-rived MCT as a Landau theory [t09/228], thusclarifying the universality of MCT predictions;in particular the square root singularity of theorder parameter, the scaling function in the βregime and the functional relation between theexponents dening the α and β timescales. Incollaboration with J.-P. Bouchaud, A. Lefèvreand M. Tarzia, we developed [t09/229] a the-ory of non-linear responses of super-cooled liq-uids based on MCT. We obtained the frequencyand temperature dependence of the non-linearresponse in the α and β-regimes. Our resultsdemonstrate that supercooled liquids are char-acterized by responses to external perturbationsthat become increasingly non-linear as the glasstransition is approached.

C.4.6 Dynamical heterogeneity in super-cooled liquids (G. Biroli)

In collaboration with experimentalists ofSPEC/CEA we showed in [t10/280] the rstevidences of growing spatial correlations at theglass transition from nonlinear response exper-iments. Experimental results on non-linear di-electric susceptibility were obtained and com-pared to theoretical results obtained previously,see [t09/229]. In collaboration with R. Cande-lier et al. we identied [t09/224] by numericalsimulations of a two dimensional glass form-ing liquid the pattern of microscopic dynamicalrelaxation: On short timescales, bursts of ir-reversible particle motion, called cage jumps,aggregate into clusters. On larger time scales,clusters aggregate both spatially and temporallyinto avalanches. This propagation of mobility,or dynamic facilitation, takes place along thesoft regions of the systems. Our results charac-terize the way in which dynamical heterogeneityevolves in moderately supercooled liquids andreveal that it is astonishingly similar to the onefound for dense glassy granular media.

C.4.7 Glassy dynamics as a melting pro-cess (L. Zdeborova)

The following properties are in the present lit-erature associated with the behavior of super-












cooled glass-forming liquids: faster than expo-nential growth of the relaxation time, dynamicalheterogeneities, growing point-to-set correlationlength, crossover from mean eld behavior to ac-tivated dynamics. In [t11/071] we argue thatthese properties are also present in a much sim-pler situation, namely the melting of the bulkof an ordered phase beyond a rst order phasetransition point. We discuss in detail the analo-gies and the dierences between the glass andthe bulk melting transitions. In [t11/072] wepush this analogy even further and show thatfor a class of Ising spin models undergoing a rstorder transition - namely p-spin models on theso-called Nishimori line - the melting dynam-ics can be exactly mapped to the equilibriumdynamics. In this mapping the dynamical -ormode-coupling- glass transition corresponds tothe spinodal point, while the Kauzmann transi-tion corresponds to the rst order phase tran-sition itself. Both in mean eld and nite di-mensional models this mapping provides an ex-act realization of the random rst order theoryscenario for the glass transition.

C.4.8 Aging is - almost - like equilibrium(A. Lefèvre)

Mean eld models have played a key role in un-derstanding the slowing down of dynamics inglassy systems. However, there remained a fewincertainties in the solution of the resulting dy-namical equations. Indeed, the decay of theslow, aging part, of the relaxation of two pointscorrelations was only characterized through un-determined scaling functions - the so-called timere-parametrization invariance. In collaborationwith A. Andreanov, we focused on the regimeseparating the equilibrium part of the relaxationand the aging one, and showed that it in factincludes all relevant information about ageingdynamics. We showed that knowing the relax-ation of the energy is enough for characteriz-ing the whole dynamics of all correlation func-tions, which in particular lead to a conjectureabout the stretched exponential decay of corre-lators at long times. Making one step further, in[t09/267], we showed that slow dynamics belowand above the ideal glass transition are iden-tical provided the distance to the low energymetabassins are identied. In other words, at agiven energy, dynamics probe the same regionsof the energy landscape, be they above or belowthe critical point. This strong results makes itpossible to fully characterize - within mean eldmodels - the crossover from ageing to equilib-rium when ageing is interrupted and to compute

the asymptotic behaviour of the crossover timescale. It also provides natural scaling conjec-tures for the growing of a dynamic correlationlength in the glassy phase, as a function of theage of the sample.

C.5 Granular media and the jam-ming transition

C.5.1 Jamming transition of granularmaterials and relationship withglassy dynamics (G. Biroli)

In collaboration with the experimental group ofOlivier Dauchot in SPEC/CEA, we studied sev-eral aspects of the Jamming transition of gran-ular materials. We identied [t09/230, t08/030]from experiments the pattern of microscopic dy-namical relaxation and their relationship withdynamical heterogeneities. We found resultsvery similar to the ones obtained for super-cooled liquids [t09/224]. Moreover we studiedtheir evolution approaching the jamming transi-tion in [t09/223]. Our main nding is that dy-namical facilitation becomes less conserved andplay a lesser role for structural relaxation ap-proaching the transition. In [t10/275, t08/030]we studied whether the dynamics of granularmedia in the jammed, glassy region can be de-scribed in terms of modes, as proposed inthe literature. Analyzing experimental resultsobtained by the Saclay group, we found thatthe description in terms of modes is question-able. Modes cannot even be precisely denedclose to the jamming transition because the sys-tem is not stable enough and instead it dis-plays frequent cracks. The statistical analy-sis performed in [t10/275] is corroborated bythe analysis [t10/282] of the super-diusive mo-tion detected close to the transition. This corre-sponds to a genuine Levy ight, but with jumpsize very small compared to the diameter of thegrains. These jumps are random in time, butcorrelated in space, and can be interpreted asmicro-crack events at all scales.

C.5.2 Slow dynamics of a granular col-umn (J.-M. Luck)

The study of the slow orientational dynamics ofa column of interacting grains has been com-pleted with the exploration of the full param-eter space of the model. The resulting fourdynamical regimes (ballistic, logarithmic, acti-vated, and glassy) have been characterized bymeans of the distribution of the jamming time ofzero-temperature dynamics, and of the statisticsof attractors reached by the latter, in perspectivewith the Edwards hypothesis. Shape eects are













most pronounced in the cases of strong and weakfrustration, and essentially disappear around amean-eld point [t10/082]. Two reviews on theseand related matters have appeared in popularjournals [t08/113, t09/064].

C.6 Spin glasses

C.6.1 The nature of the spin glass phasein low dimension (C. De Dominicis)

One of the most debated point in spin-glass the-ory has to do with the fact that there are two,apparently, unrelated approaches to look at theproblem: In innite dimensions, almost all ex-perts agree: Parisi's replica approach exactlysolves the problem posed by the SK model. Inlow dimension (2 ≤ d ≤ 8) the droplet theoryput forward by Fisher and Huse and by Brayand Moore oers an other way, with the con-cept of scale dependent coupling. And for thelast authors a proposal to keep the Parisi ap-proach down to 6 dimensions and the dropletone at and below d = 6. Here we will be essen-tially using the tools of replica calculus (mostlyvia replica Furrier transforms), and we will con-struct the free energy as a stationary functionalof the eld Qa,b ≡ < SaSb >. We try to keeptrack of the Qa,b matrix, when deriving compo-nents of the Hessian (second functional deriva-tive) whose eigenvalues are the masses of theQa,b propagators. Keeping in mind that stabil-ity requires nonnegative (masses) eigenvalues.

We [t09/279] write the overlap matrixQa,b asQa,b = δa,b+q(1−δa,b)+δQa,b. The original SKsolution is given by δQa,b = 0. Here we expandin powers of δQa,b and we keep up to 4th orderin δQ (the lowest order accepting solutions withfull replica symmetry breaking (FRSB) ansatz).The surprise is that the FRSB solution existsonly for 0.549.. ≤ T < Tc = 1 Besides, the Q(x)obtained does not vanish with x (as in the ex-act Parisi solution). If we work in zero magneticeld (q = 0) and Qa,b = δa,b + δQa,b now Q(x)vanishes with x, but the FRSB solution existsonly for 0.915.. ≤ T < Tc = 1 and thus cannotbe used to study the system close to T = 0.

We now work [t09/272] with two elds: TheIsing eld σa and a constraint eld λa that willforce the spins σa to remain close to ±1. The(doubly) stationary free energy (with respect toboth, elds and correlations) is then organizedaccording to the number of loops. The simplestcontribution is given by a two loop diagram.However, it turns out that at low enough T theconstraint becomes ineective and a FRSB so-lution exists only for 0.783.. ≤ T < Tc = 1.Perhaps it would be worth going one more step

in the loop expansion e.g. by keeping all graphswith a single loop of spin eld propagators, totest how the constraint is then taken into ac-count.

In [t10/274] and [t11/101], the structure ofthe Hessian of the SK model is investigated nearzero T . The eigenvalues of the Hessian are themasses of the bare propagators in the expansionaround the mean eld solution of Parisi. In theT 1 limit, two regions can identied:i) for x close to zero (x is the overlap variable, inQ(x)) the spectrum of the Hessian remains nontrivial and maintains the FRSB structure foundat higher T ,ii) for T x ≤ 1, as T → 0 the components ofthe Hessian become insensitive to changes of theoverlaps, the bands, typical of the FRSB, col-lapse. In this region most eigenvalues vanish, ex-cept longitudinal masses that remains positive.

In the T → 0 limit, the width of the (inner)rst region shrinks to zero and in the (outer)other region positive and null eigenvalues sur-vive. In the last work a way of computing mul-tiple spin averages (e.g. < SaSbScSd >) is de-tailed, exhibiting for example the dierence ordierential equations giving birth to multispinaverages of the free energy itself.

C.6.2 Finite size scaling in the SK model(A. Billoire)

In collaboration with T. Aspelmeier, E. Marinariand M. Moore [t07/147] we argue that when thenumber of spins N in the SK model is nite, theParisi scheme can be terminated after K replica-symmetry breaking steps, where K(N) ∝ N1/6.We have checked this idea by Monte Carlo sim-ulations: we expect the typical number of peaksand features R in the (non-bond averaged) Parisioverlap function PJ(q) to be of order 2K(N),and our counting (for samples of size N upto 4096 spins) gives results which are consis-tent with our arguments. We can estimate theleading nite size correction for any thermo-dynamic quantity by nding its K dependencein the Parisi scheme and then replacing K byK(N). Our predictions of how the Edwards-Anderson order parameter and the internal en-ergy of the system approach their thermody-namic limit compare well with the results of ourMonte Carlo simulations. The N-dependence ofthe sample-to-sample uctuations of thermody-namic quantities can also be obtained; the totalinternal energy should have sample-to-sampleuctuations of order N1/6, which is again con-sistent with the results of our numerical simula-tions.










C.6.3 Distribution of relaxation time inthe SK model (A. Billoire)

In [t10/157] numerical data on the proba-bility distribution of the equilibrium relax-ation time of the Sherrington-Kirkpatrick modelare presented, for several values of the sys-tem size N and temperature T . The wholedistribution scales with the scaling variableN1/3(Tc − T ) strengthening the belief that in-deed E(ln τ(N)) ∝ N1/3 in the spin glass phase.

In [t10/179] using results of a MonteCarlo simulation of the Sherrington-Kirkpatrickmodel, we try to characterize the slow disordersamples, namely we analyze visually the corre-lation between the relaxation time for a givendisorder sample J with several observables of thesystem for the same disorder sample. For tem-peratures below Tc but not too low, fast samples(small relaxation times) are clearly correlatedwith a small value of the largest eigenvalue ofthe coupling matrix, a large value of the site av-eraged local eld probability distribution at theorigin, or a small value of the squared overlap< q2 >. Within our limited data, the correla-tion remains as the system size increases but be-comes less clear as the temperature is decreased(the correlation with < q2 > is more robust).There is a strong correlation between the valuesof the relaxation time for two distinct values ofthe temperature, but this correlation decreasesas the system size is increased. This may indi-cate the onset of temperature chaos.

C.6.4 Large random correlations in indi-vidual mean eld spin glass sample(A. Billoire)

In collaboration with I. Kondor, J. Lukic and E.Marinari [t10/158] we argue that complex sys-tems must possess long range correlations andillustrate this idea on the example of the meaneld spin glass model. Dened on the completegraph, this model has no genuine concept ofdistance, but the long range character of cor-relations is translated into a broad distributionof the spin-spin correlation coecients for al-most all realizations of the random couplings.When we sample the whole phase space we ndthat this distribution is so broad indeed thatat low temperatures it essentially becomes uni-form, with all possible correlation values appear-ing with the same probability. The distributionof correlations inside a single phase space valleyis also studied and found to be much narrower.

C.6.5 Spin glass phase in random eldIsing model, possible or not (L.Zdeborova)

Krzakala, Ricci-Tersenghi and Zdeborova haverecently closed a twenty years open question byproving that the random eld Ising model withnon-negative interactions and arbitrary externalmagnetic eld on an arbitrary lattice does nothave a static spin glass phase. In [t11/070] wegeneralize this proof to a soft scalar spin ver-sion of the Ising model: the Ginzburg-Landaumodel with random magnetic eld and randomtemperature-parameter. We do so by provingthat the spin glass susceptibility cannot divergeunless the ferromagnetic susceptibility does. In[t11/073] we investigate in detail the phase dia-grams of the p-body ±J Ising model with andwithout random elds on random graphs withxed connectivity. One of our most interest-ing ndings is that a thermodynamic spin glassphase is present in the three-body purely ferro-magnetic model in random elds.

C.7 Other disordered systems

C.7.1 Phase transitions of random sys-tems (T. Garel and C. Monthus)

In the presence of frozen disorder, phase tran-sitions are governed by the renormalization ofprobability distributions (in contrast to puresystems where only a few coupling constantsare relevant). It is thus instructive to studythese transitions on diamond lattices where ex-act renormalization for the relevant probabilitydistributions can be written: this approach hasbeen applied to disordered polymers [t07/130]and to random ferromagnets [t07/152]. It is alsouseful to obtain exact results on the Cayley tree[t09/028].

C.7.2 Disorder-dominated phases of ran-dom systems (T. Garel and C. Mon-thus)

In the low-temperature disorder-dominatedphases of various random models (directed poly-mer, ferromagnetic random Potts model, Isingspin-glasses), the free-energy cost F (L) of an ex-citation of length L presents uctuations thatgrow as a power-law ∆F (L) ∼ Lω with the so-called droplet exponent ω > 0. The tails ofthe probability distribution Π(x) of the rescaledfree-energy cost x = (FL − FL)/Lω are governedby two exponents (η−, η+) dened by ln Π(x →±∞) ∼ −|x|η± . We have proposed simple rela-tions between these tail exponents (η−, η+) andthe droplet exponent ω [t07/133]. For the statis-











tics of global observables in disordered systems,like the distribution of the ground state energyover the samples, we have similarly proposed toanalyse the matching between typical uctua-tions and large deviations to obtain relations be-tween exponents [t10/009].

C.7.3 Random walks in random media(T. Garel and C. Monthus)

For random walks in random media, we have ex-tended the strong disorder renormalization ap-proach to the two-dimensional case [t10/002].For the statistics of rst-passage times, we havealso studied the exact renormalization of the as-sociated backwards master equations [t10/004].The response to a small external force is foundto be anomalous [t10/102].

C.7.4 Non-equilibrium dynamics of dis-ordered systems (T. Garel and C.Monthus)

For the dynamics of many-body disorderedsystems, we have introduced a strong disor-der renormalization procedure in congurationspace [t08/048, t08/092]. In particular, we havedescribed in [t08/122] how to construct explic-itly the valleys separated by the highest dynam-ical barriers. In [t09/208], we have introducedan eigenvalue method to compute the largest re-laxation time of nite systems. For the non-equilibrium dynamics of polymers and interfacesin random media, we have proposed a conjec-ture for the barrier exponent ψ governing theslow activated dynamics [t08/004]. For driveninterfaces in random media, we nd an anoma-lous zero-velocity phase at small external force[t08/148].

C.8 Hard optimization problems(L. Zdeborova)

The Boolean satisability problem is a bench-mark of hard optimization problem in computerscience. In [t11/067] we study the adversar-ial satisability problem, where the adversarycan choose whether variables are negated inclauses or not in order to make the resultingformula unsatisable. This is one case of a gen-eral class of adversarial optimization problemsthat often arise in practice and are algorithmi-cally much harder than the standard optimiza-tion problems. We use the cavity method tocompute large deviations of the entropy in therandom satisability problem with respect to thenegation-congurations.

C.9 Networks, theoretical epi-demiology, quantitative ur-banism

C.9.1 Spatial networks (M. Barthélemy)

Complex systems are very often organized underthe form of networks where nodes and edges areembedded in space. Transportation and mobil-ity networks, Internet, mobile phone networks,power grids, social and contact networks, neuralnetworks, are all examples where space is rele-vant and where topology alone does not containall the information. Characterizing and under-standing the structure and the evolution of spa-tial networks is thus crucial for many dierentelds ranging from urbanism to epidemiology.An important consequence of space on networksis that there is a cost associated to the lengthof edges which in turn has dramatic eects onthe topological structure of these networks. Wewill expose thoroughly the current state of ourunderstanding of how the spatial constraints af-fect the structure and properties of these net-works. We will review the most recent empiricalobservations and the most important models ofspatial networks. We will also discuss variousprocesses which take place on these spatial net-works, such as phase transitions, random walks,synchronization, navigation, resilience, and dis-ease spread.[t11/027]

C.9.2 Fluctuation eects in metapopula-tion models: percolation and pan-demic threshold (M. Barthélemy, C.Godrèche, J.-M. Luck)

Metapopulation models provide the theoreticalframework for describing disease spread betweendierent populations connected by a network. Inparticular, these models are at the basis of mostsimulations of pandemic spread. They are usu-ally studied at the mean-eld level by neglectinguctuations. Here we include uctuations in themodels by adopting fully stochastic descriptionsof the corresponding processes. This level of de-scription allows to address analytically, in theSIS and SIR cases, problems such as the exis-tence and the calculation of an eective thresh-old for the spread of a disease at a global level.We show that the possibility of the spread atthe global level is described in terms of (bond)percolation on the network. This mapping en-ables us to give an estimate (lower bound) forthe pandemic threshold in the SIR case for allvalues of the model parameters and for all pos-sible networks.[t10/049]















Figure C.2: Example of spatial networks. (A) Manhattan power grid. (B) European pipelines.(C) Roads and streets in San Francisco, (D) Tokyo subway.

C.9.3 Disentangling collective trendsfrom local dynamics (M. Barthé-lemy)

A single social phenomenon (such as crime,unemployment or birth rate) can be observedthrough temporal series corresponding to unitsat dierent levels (cities, regions, countries...).Units at a given local level may follow a col-lective trend imposed by external conditions,but also may display uctuations of purely lo-cal origin. The local behavior is usually com-puted as the dierence between the local dataand a global average (e.g. a national average),a view point which can be very misleading. Wepropose here a method for separating the localdynamics from the global trend in a collectionof correlated time series. We take an indepen-dent component analysis approach in which wedo not assume a small unbiased local contribu-tion in contrast with previously proposed meth-ods. We rst test our method on synthetic seriesgenerated by correlated random walkers. Wethen consider crime rate series (in the US andFrance) and the evolution of obesity rate in the

US, which are two important examples of soci-etal measures. For crime rates, the separationbetween global and local policies is a major sub-ject of debate. For the US, we observe largeuctuations in the transition period of mid-70'sduring which crime rates increased signicantly,whereas since the 80's, the state crime rates aregoverned by external factors and the importanceof local specicities being decreasing. In thecase of obesity, our method shows that externalfactors dominate the evolution of obesity since2000, and that dierent states can have dierentdynamical behavior even if their obesity preva-lence is similar.[t09/251]

C.9.4 Structure of urban movements:polycentric activity and entangledhierarchical ows (M. Barthélemy)

The spatial arrangement of urban hubs and cen-ters and how individuals interact with these cen-ters is a crucial problem with many applicationsranging from urban planning to epidemiology.We utilize here in an unprecedented manner thelarge scale, real-time `Oyster' card database ofindividual person movements in the London sub-



way to reveal the structure and organization ofthe city. We show that patterns of intra-urbanmovement are strongly heterogeneous in termsof volume, but not in terms of distance travelled,and that there is a polycentric structure com-posed of large ows organized around a limitednumber of activity centers. For smaller ows,the pattern of connections becomes richer andmore complex and is not strictly hierarchicalsince it mixes dierent levels consisting of dier-ent orders of magnitude. This new understand-ing can shed light on the impact of new urbanprojects on the evolution of the polycentric con-guration of a city and the dense structure ofits centers and it provides an initial approach tomodeling ows in an urban system.[t10/113]

C.9.5 Fluctuations, records, and leadersin growing network models (C. Go-drèche, H. Grandclaude, J.-M. Luck)

Growing networks have become increasinglypopular. They provide a natural explanation forthe two most salient features observed in realnetworks, either natural or man-made: small-world eect (the diameter of the network growsvery slowly with the number of nodes, typicallylogarithmically) and scalefreeness (the degreesof nodes have a broad distribution, falling o asa power law). In simple growing network modelswith preferential attachment, a new node entersat each time step, and attaches to one earliernode according to some stochastic rules. Thenetwork thus obtained is a random tree, and itssize (number of nodes) is nothing but its age(the time elapsed since it started to grow). Bian-coni and Barabási (BB) have introduced a veryfruitful model, where the attachment probabil-ity to a given node depends on two ingredients:a dynamical one (its degree at the attachmenttime) and an intrinsic one (its quality or tness,modeled as quenched disorder). The relative im-portance of these two eects is measured by atemperature. The most salient feature of theBB model is that it may have, depending ondisorder, a condensation transition at some -nite temperature. The earlier Barabási-Albert(BA) model is recovered at innite temperature,while a novel phenomenon takes place in the low-temperature condensed phase, as some nodes at-tract a nite fraction of all the connections.

We have devoted several works to the studyof uctuations in various models of growing net-works, including the BA and BB models. Ourmain motivation was to aim at a better un-derstanding of the dynamics in the condensedphase, where the most important part is played

by high-degree nodes. We have thus paid specialattention to the leader, i.e., the node whose de-gree is the largest at a given time. More specif-ically, we have performed a systematic investi-gation of nite-size eects on the distribution ofthe node degrees. These eects have been shownto exhibit dierent behaviors in three regimesin the size-degree plane: stationarity, nite-sizescaling, large deviations [t09/100]. The zero-temperature limit of the BB model has also beenexplored in depth. In this limit, the record node(the node whose tness is the best at the currenttime) attracts all the new connections, until itis outdone by a tter node. This observationled us to introduce a novel stochastic growthmodel, the record-driven growth process. Manyfeatures of the latter can be analyzed by exactmethods, based on the statistics of records. Togive one example, any record node has a chanceω = 0.624329988... to eventually become theleader of the network, where ω is the Golomb-Dickman constant which arises in various prob-lems of combinatorics, including random per-mutations [t08/142]. More generally, we haveinvestigated leaders and lead changes in grow-ing networks, by exploring many quantities con-cerning either the leader at a given time (itsage, the distribution of its degree, the numberof co-leaders if any) or the whole history of leadchanges (numbers of lead changes and of distinctleaders). For the BB model, irrespectively of theexistence of a condensation transition, new lead-ers appear endlessly at any temperature, albeitextremely slowly, on a doubly logarithmic timescale, so that the leader of today is the recordof old. This analysis also provides a novel pic-ture for the dynamics in the condensed phase.The latter is characterized by an innite hier-archy of condensates, whose relative sizes arenon-self-averaging and keep uctuating forever[t09/184, t10/078].

C.10 Heavy fermion physics

C.10.1 The modulated spin liquid inURu2Si2 (C. Pépin)

In [t10/288], we get involved in the study ofURu2Si2, a heavy fermion compound which rep-resents one of the oldest mystery in condensedmatter physics, and which has received a re-newed attention recently, due to a body of newand creative experimental work. The pure com-pound shows a pronounced second order phasetransition at T0 = 17K towards a mysterious or-dered phase dubbed Hidden Order (HO). Theamount of entropy lost at the transition is large,of the order of 0.3RLn2. There is a large amount








of evidence that the transition is not of magneticcharacter and that a large number of carriers dodisappear at T0. Moreover, recent studies showa striking similarity between the hidden orderphase and a large moment anti-ferromagneticphase which is revealed under a small amount ofuni-axial pressure. In our work, we exploit thisremarkable similarity between the two phases,and we suggest a Resonant Valence Bond (RVB)spin liquid as a strong candidate for the hiddenorder, modulated in the dual lattice. This orderparameter has the particularity to be very hardto detect, as all the spin liquid phases, besidesthe fact that, since it breaks the Z4 symmetryof the lattice, it leads to a pronounced secondorder phase transition at T0 [instead of a cross-over]. The Modulated Spin Liquid shows strongsimilarities with a corresponding antiferromag-netic phase, and can be considered as the RVB-parent of the antiferromagnet. We intend toinvestigate further the properties of this inter-esting new candidate, and in particular, in thenear future to construct a realistic model for thedynamic spin susceptibility, in order to the ableto address the extensive neutron scattering re-sults already available.

C.10.2 Kondo breakdown in 3He bi-layers (A. Benlagra, C. Pépin)

In [t08/179], [t08/180] and [t10/286], we applyour newly developed model of the Kondo break-down, originally conceived for heavy fermions,to a recent experiment by the group of J. Saun-ders in London [M. Neumann et al., Science,317 1356 (2007)]. In this experiment a Quan-tum Critical Point (QCP) of unknown nature isrevealed through specic heat and NMR mea-surements in 3He bi-layers. Atoms of 3He aredeposed on a substrate made of two layers of4He itself deposed on graphite. As the coverageof the two last layers is slowly varied, one ob-serves, at a critical coverage of 9.2 nm−1 a sud-den increase of the static susceptibility. At a bitbigger coverage, of nc = 10 nm−1 the eectivemass is shown to increase by a factor of 20. Thecritical coverage nc is consequently identied asthe quantum critical coverage of the system. Inour papers we address this experiments by map-ping the two layers system onto an Anderson lat-tice with inter-layer Coulomb repulsion betweenthe 3He fermions. We make the assumption thatthe experimentally revealed QCP corresponds toa Mott localization of the atoms on the secondlayer, while the ones in the rst layer have al-ready localized at lower doping. Applying ourEliashberg theory of the Kondo breakdown, we

were able to quantitatively account for the vari-ation of the eective mass, and of the transitiontemperature as a function of the coverage. Wereproduce as well the variation of the activationgap with coverage, although we are short of afactor of 10, for the quantitative value of thegap.

C.10.3 Kondo breakdown and selec-tive Mott transition in heavyfermions (A. Benlagra, K.-S. Kim, C.Pépin)

The breakdown of the Landau theory of theFermi liquids, experimentally observed in heavyfermion compounds still remains a mystery forthe theoretician: The resistivity is linear (orquasi-linear) in temperature for many com-pounds around zero temperature phase transi-tions and the specic heat coecient doesn't sat-urate (as it should do in a well behaved Fermiliquid). For a very long time, we have looked fora QCP of magnetic nature to explain the unusualproperties of these materials, but none of themagnetic QCP for itinerant electrons provideda strong enough violation of the Fermi liquidtheory to explain the experiments. New exper-imental observations and band structure stud-ies showed recently that the compound Yb Rh2

Si2 doped with a small amount of Ge had morevalence uctuation that one would expect for atrue heavy Fermi compound. This incited us tolook for a new type of QCP, not directly asso-ciated to magnetic transitions. We found one,in the Kondo-Heisenberg lattice, for which theeective hybridization between the two type ofelectrons, the localized spinons and the conduc-tion electron band goes to zero at zero tempera-ture. At this xed point, the Fermi surface vol-ume changes abruptly while the spinon Fermisurface gets completely hot. Moreover, thisQCP has a multi-scale character, with above asmall energy scale E∗, a marginal Fermi liquidregime, including a resistivity in T LogT in 3 di-mensions, and logarithmically divergent specicheat variation. This very interesting QCP, thatwe called the Kondo breakdown is the rst ef-fective eld theory which leads to a regime quasi-linear in temperature for the resistivity in 3 D.

In addition we found that a phase with an hy-bridization modulated in space, analogous to theFulde Ferell Larkin Ovshinikov superconductorcan occur. It's again the rst evidence for sucha phase in heavy fermion compounds.

In a series of eight papers [t08/267, t08/268,t08/178, t09/026, t08/269, t09/275, t10/019,t10/287] we explore the testability of our the-













ory for various experimental probes. the mainidea underlying those tests is that the Kondobreakdown model is a good model for transportproperties whereas it misses the eect of mag-netism in the system. We consider the proxim-ity to the selective Mott transition, as the mainprovider for scattering events, so that this mech-anism dominates the transport. The system hasthe peculiarity that it has two types of electrons,ones at the brink of localization [the f -electrons]and ones very localized [the c-electrons]. Crit-ical scattering of the c- electrons through thelattice of f-electrons gets a backscattering com-ponent and hence a mechanism to decay the cur-rent. The various transport and thermodynamicprobes that we have examined count a study ofthe Wiedemann-Franz ratio, one of the Grüney-sen ratio, as well as a quite systematic studyof prediction of the Seebeck coecient and thethermopower. In both those cases, we foundthat the model can bring some qualitative pre-dictions.

C.11 High temperature supercon-ductors and Mott transition

C.11.1 Cuprate superconductors (M. Fer-rero, O. Parcollet)

One of our directions of research consists in de-veloping systematic hybrid methods to solve mi-croscopic models of strongly correlated systems,like e.g. the Hubbard model, or the 3 bandsmodel of cuprates. Indeed, direct numerical ap-proaches like Quantum Monte Carlo have failedto solve these models because e.g. of the fa-mous sign problem (in contrast to their bosonicanalogues). New hybrid methods are there-fore emerging, mixing analytical and physicalinsights with innovative algorithms in order tobypass this major diculty, and making the tra-ditional distinction between numerical experi-ment and theory largely obsolete.

Roughly speaking, one can distinguish twostrategies: in the top-to-bottom strategy, onestarts from high temperature (or high doping)regions where the physics is simpler, and pro-gresses towards lower temperature. This followsin spirit the Renormalization Group idea : startfrom high energy physics, and let progressivelythe low energy degrees of freedom emerge; in thebottom-to-top strategy, one tries to understandthe zero temperature ground state, its quantumproperties, and then deduce the nite temper-ature properties from there. Dynamical MeanField Theory (DMFT) and its extensions imple-ment the rst strategy, while DMRG and exten-

sions are an example of the second one.

Cluster DMFT methods are technically asystematic expansion of the two-particle ir-reducible Luttinger-Ward-Baym-Kadano func-tional around the atomic limit. Physically,DMFT can also be seen as a quantum gener-alization of the classic Weiss mean eld for theMott transition, mapping a lattice problem ontoan eective quantum impurity problem (Ander-son model) in a self-consistent bath. Its clus-ter extensions then map the lattice model ontoN such coupled impurities (in their bath). Thecluster size N is the control parameter : it inter-polates from the mean eld (N = 1) to the exactsolution of the lattice model (N →∞), and de-termines the resolution in momentum space ofthe method. Cluster methods open a route toa controlled solution of the many-body models,starting from high temperature or doping, whereDMFT is only weakly corrected. Physically,this strategy is well-suited for many stronglycorrelated materials since they have many dif-ferent possible instabilities at low temperature,while their intermediate temperature propertiescan be expected to be more universal. Clustermethods exist in various forms. For example,in the so-called Dynamical Cluster Approxima-tion version, the Brillouin zone is tiled with a -nite number of patches, on which the electronicself-energy is approximated by a function of fre-quency only (constant in momentum). The big-ger the cluster is, the more rened the resolution,as illustrated on Fig. C.3.

Our work has followed two complementarydirections. First, in [t08/192, t09/114], using aminimal two sites cluster approach (the left pic-ture on Fig. C.3), we proposed a very simplieddescription of the normal phase of cuprates interms of a selective Mott transition in momen-tum space, where the nodal regions stay metallicwhile the antinodal regions become insulating.Second, we conrmed this picture by compar-ing systematically the solution for various clus-ter sizes, up to the largest cluster doable withreasonable resources (16 sites), e.g. those repre-sented on Fig. C.3 [t09/105, t09/129, t10/122](the cluster size is limited in practice by theresurgence of the sign problem). Those cal-culations were made accessible by huge recentprogress in algorithms, including our new con-tinuous time quantum Monte Carlo CT-AUXalgorithm designed for cluster problems, which isnow used by several groups worldwide [t08/086].Finally, the consequences of this physical picturefor c−axis optical conductivity were also inves-tigated, in collaboration with the group of D.








(π, π)

(0, 0)

(0, π)

(π, 0)(0, 0)

(π, π)

(0, 0)

(π, π)

(π/2, π/2)

(π, 0)

(0, 0)

(π, π)

Figure C.3: The momentum resolution in the Brillouin zone for some Cluster DMFT methodswith 2,4,8, and 16 patches, from [t10/122].

Basov (San Diego, USA) [t10/259]. The con-sequences of this idea in the superconductingphase is currently under investigation, followingthe rst results obtained with small clusters in[t07/084].

C.11.2 Iron-based superconductors (M.Ferrero, O. Parcollet)

In 2009, the question of the degree of correlationof the new iron-based (pnictides) superconduc-tors was strongly debated, in particular in theDMFT community. Therefore, in [t09/115], westudied the strength of electronic correlations inone of the iron-based (pnictides) superconduc-tors, using the rst implementation of an ab-initio approach combining the local density ap-proximation (LDA) and Dynamical Mean FieldTheory in the framework of the full-potential lin-ear augmented plane waves (FLAPW) method.Our ndings support the physical picture of ametal with intermediate correlations.

C.11.3 Eect of crystal eld splitting onthe Mott transition (M. Ferrero, O.Parcollet)

In [t08/035], we investigated the eect ofthe crystal-eld splitting on the Mott metal-insulator transition in correlated materials suchas transition-metal oxides. At large values of thesplitting, a transition from a two-band to a one-band metal, as the on-site repulsion increases, isfollowed by a standard Mott transition for theremaining band. At small values of the splitting,a direct transition from a two-band metal to aMott insulator with partial orbital polarizationis found.

C.12 Antiferromagnets and spinliquids

C.12.1 Classical frustrated spin systems(G. Misguich)

In [t08/206] we explored the phase diagram of atwo-dimensionnal classical spin-like model whichcaptures the physics of non-collinear antiferro-magnets. In such systems the order parameteris not a simple vector but a matrix in O(3). Atnite temperature the magnetic ordering is for-

bidden by the Mermin-Wagner theorem but thechirality degrees of freedom associated to thetwo connected components (∼ SO(3)) of O(3)gives rise to a nite temperature transition (dis-crete symmetry breaking). Using Monte-Carlosimulations (Wang-Landau) we explained thatthe particular attraction between the chiralitydomain walls and the Z2 vortices associated toSO(3) is a mechanism which favors the rst-order nature of the chiral transition in frustratedspin systems.

In [t11/103] we introduced some classicalspin structures which respect all the lattice sym-metries modulo global 0(3) spin transformations,cf Fig. C.4. Dubbed regular magnetic orders(RMO), they are dened as spin congurationsfor which any lattice symmetry (translations,etc.) can be absorbed by a global spin rota-tion in O(3). We show how to construct thesestates for any given lattice using simple grouptheory arguments. From a physical point ofview, we showed that RMO are ground-statesof many frustrated Heisenberg models, includingthose for which the energy minimization cannotbe done analytically.

C.12.2 Quantum dimer models (G. Mis-guich)

Heisenberg models oer accurate descriptions ofmany antiferromagnetic insulators but in severalcases, quantum uctuations drive the systemto phases without any magnetic order, even atT = 0. Those phases, so called spin-liquids, arenot easily described directly in terms of the spindegrees of freedom but they can be qualitativelyunderstood through simplied models where thebasic degrees of freedom are pairs of spins cou-pled in a singlet state, also called valence-bond,or dimer. A quantum dimer model (QDM) de-scribes the dynamics of these (short-ranged) sin-glet pairings. In collaboration with F. Mila(Lausanne), we investigated the liquid phase ofthe QDM on the triangular lattice [t07/159].There, we proposed some variational approxi-mation to describe the gapped Z2 vortex exci-tations (dubbed visons) which caracterize thisphase.









Figure C.4: Spin directions of a twelve-sublattice cuboc state on a kagome network

C.12.3 Quantum spin liquids (G. Mis-guich)

[t07/161], [t08/250] and [t11/018] correspond tothree book chapters (one in collaboration withC. Lhuillier) on quantum spin liquids and frac-tionalization in quantum antiferromagnets.

C.12.4 The valence bond glass phase (G.Biroli)

In collaboration with M. Tarzia [t08/150] weshowed that a new glassy phase can emergein presence of strong magnetic frustration andquantum uctuations. It is a Valence BondGlass. We studied its properties solving theHubbard-Heisenberg model on a Bethe latticewithin the large N limit introduced by Af-eck and Marston. This new quantum glassyphase has no electronic or spin gap (althougha pseudo-gap is observed), it is characterizedby long-range critical valence bond correlationsand is not related to any magnetic ordering.This phase was recently found in experimentsby Mclaughlin et al. in double PerovskiteBa2YMoO6.

C.12.5 Dimers on the cubic lattice (G.Misguich, V. Pasquier)

[t08/079] is the continuation of a previous work[t06/197] concerning a phase transition in athree-dimensional classical dimer model on thecubic lattice. Each dimer occupies two sites insuch a way that each site is covered by one andonly one dimer. In addition to this hard-core

constraint, an energy equal to -1 times the num-ber of square plaquettes with two parallel dimersis associated to each conguration. At low tem-perature the plaquette interaction favors a reg-ular (crystalline) arrangements of dimers. Athigh temperature the dimers are no longer or-dered but their correlations decay algebraicallywith distance. The later phase has been dubbedCoulomb phase. The precise nature of thetransition between the crystal and the Coulombphase has not yet been fully elucidated and thiswork presents a detailed numerical analysis ofthe correlation functions at the transition.

C.12.6 Vacancy localization in thesquare dimer model (J. Bouttier,E. Guitter)

In [t07/070], we study the classical dimer modelon a square lattice with a single vacancy by de-veloping a graph-theoretic classication of theset of all congurations which extends the span-ning tree formulation of close-packed dimers.With this formalism, we can address the ques-tion of the possible motion of the vacancy in-duced by dimer slidings. We nd a probabil-ity 57/4 − 10

√2 for the vacancy to be strictly

jammed in an innite system. More generally,the size distribution of the domain accessible tothe vacancy is characterized by a power law de-cay with exponent 9/8. On a nite system, theprobability that a vacancy in the bulk can reachthe boundary falls o as a power law of thesystem size with exponent 1/4. The resultant








weak localization of vacancies still allows for un-bounded diusion, characterized by a diusionexponent that we relate to that of diusion onspanning trees.

C.13 Ultra-cold atomic gases

C.13.1 Fermionic Mott transition (M.Ferrero, O. Parcollet)

In [t08/191], we performed a theoretical studyof a fermionic gas with two hyperne states con-ned to an optical lattice, in order to discuss therealization of the fermionic Mott transition inrecent experiments (Joerdens et al., 2008). Wederived a generic state diagram as a function ofinteraction strength, particle number, and con-ning potential. We discussed the central den-sity, the double occupancy and their derivativesas probes for the Mott state.

C.13.2 Polarized superuidity in the at-tractive Hubbard model withpopulation imbalance (M. Ferrero,O. Parcollet)

In [t08/190], we studied a two-component Fermisystem with attractive interactions and dierentpopulations of the two species in a cubic lattice.For an intermediate coupling we found a uni-formly polarized superuid which is stable downto very low temperatures. The momentum dis-tribution of this phase closely resembles that ofthe Sarma phase, characterized by two Fermisurfaces. This phase is shown to be stabilizedby a potential energy gain, as in a BCS super-uid, in contrast to the unpolarized BEC whichis stabilized by kinetic energy.

C.14 Graphene

C.14.1 Graphene fundamental physics(C. Bena)

Graphene has been studied extensively in therecent years, especially after it became possibleto fabricate it through exfoliation. Its most fas-cinating aspect is the existence of the linearly-dispersing gapless excitations in the vicinity ofthe Dirac points. Over the past few years wehave focused on analyzing both the fundamentalphysics of graphene, as well as on making predic-tions for the local density of states measurable inSTM experiments in graphene, and on makingconnection to these experiments. Concerningthe fundamental aspects, together with G. Mon-tambaux, in [t11/079] we have addressed somesubtle fundamental issues arising in the tight-binding study of graphene, as well as of othersystems that have a crystalline structure with

more than one atom per unit cell, for which thechoice of tight-binding basis is not unique. Alsoin [t08/300], we have analyzed the real-space freeGreen's function matrix, and its analytical ex-pansions at low-energy, carefully incorporatingthe discrete lattice structure of graphene and theform of the atomic-orbital wave function, and wehave computed the real-space Green's functionin the presence of an impurity.

C.14.2 Eects of impurity scattering ingraphene on the local density ofstates (C. Bena)

We have shown that the analysis of the localdensity of states (LDOS) measurable in STMexperiments can be used to establish both thenature of the impurities, as well as the formof the full Hamiltonian of the system (and notonly the band structure). Thus in [t07/226] weshowed that the chirality of quasiparticles givesrise to a peculiar signature in the Friedel oscil-lations generated in the presence of an impu-rity, and we predicted that this signature canbe extracted from the Fourier transform of thelocal density of states. These prediction wereconrmed by the groups of P. Mallet, J. Y.Veuillen (Grenoble) and of K. Kern, I. Brihuega(Stuttgart) [t11/077]. Also, with the experimen-tal group of L. Simon (Mulhouse) in [t08/298]we showed that it is possible to analyze the real-space LDOS to retrieve information about theposition and nature of impurities in graphene. In[t09/330] we calculated the LDOS in graphenein the quantum Hall regime and showed that itcan be used to understand the form of the quasi-particle wavefunction, as well as the nature ofdisorder in graphene.

C.14.3 Modied graphene andgraphene-related materials (C.Bena)

With the experimental group of L. Simon (Mul-house), in [t10/249] we have observed a newtype of ordering in monolayer graphene with in-tercalated small gold clusters between the topmonolayer graphene and the buer layer of epi-taxial graphene. In this system we have founda strong pattern of standing waves at high en-ergies, with period twice that of the atomiclattice. A detailed analysis of the standingwave patterns using Fourier transform scanningtunneling spectroscopy suggested that this phe-nomenon can arise from a strong modicationof the band structure of graphene and (or) fromthe formation of charge density waves. Subse-quently, in [t10/251] we have studied modied












graphene in the presence of a next-to-nearest-neighbor coupling and a third-nearest-neighborcoupling. We have shown that extra Diracpoints, as well as hybrid points (the electronshave a linear dispersion along one direction anda quadratic dispersion along the perpendiculardirection) may appear in the spectrum whenlarge values of the third nearest neighbor cou-pling are considered. This in turn yields a low-ering of the energy of the Van Hove singularitiesin the graphene density of states.

C.15 Bosonic systems

C.15.1 Super-solidity in He4 (G. Biroli)

The possibility of the existence of super-solidswas discussed by Leggett and Andreev and Lif-shitz forty years ago. The rst experimental ev-idences found by Kim and Chan in 2005 trig-gered a lot of new activity, especially becausetheir results could not be explained by the theo-ries developed in the past. It is by now clear thatdisorder plays a crucial role: perfect crystals ofHe4 are not super-solid. In collaboration withJ-P. Bouchaud [t08/029] we have put forward atheory of super-solidity based on quantum plas-ticity induced by dislocations. Recent experi-ments have shown that dislocations play an im-portant role, although more results are neededto obtain a clear picture. Another possibilityput forward by Prokoev et al. is that, at leastin some experimental samples, the He4 solid is aglass and not a crystal. In collaboration withC. Chamon and F. Zamponi [t09/232] we in-troduced a model of interacting bosons in threedimensions that displays this phase unambigu-ously and that can be analyzed exactly basedon a mapping between quantum Hamiltoniansand classical Fokker-Planck operators. This pro-vides a proof that this state of matter, the super-glass, can indeed exist (our work was selectedfor a presentation on the APS journal). Lateron, in collaboration with B. Clark, L. Foini andF. Zamponi [t10/272], we investigated whetherglassiness enhances superuidity. Using an up-per bound on the superuid fraction derived byLeggett we found that this is not the case. Ourresults suggest that the experimental observa-tions of large superuid fractions in He4 aftera rapid quench correspond to samples evolvingfar from equilibrium, instead of being in a stableglass phase.

C.15.2 Bose Einstein condensation ofmagnons (G. Misguich)

TlCuCl3 is an antiferromagnetic insulator witha non-magnetic ground-state (spin singlet). The

elementary excitations (magnons) have a gapthat can be reduced by an external magneticeld. When the gap closes, the magnons con-dense. This is the onset of magnetic long-rangedorder (perpendicular to the applied eld). In[t07/160] we extended our previous calculations(based on a self-consistent Hartree-Fock calcu-lation and a realistic dispersion relation of themagnons) to compare the computed magnetiza-tion curves with those measured experimentallyin the group of H. Tanaka in Tokyo.

C.16 Out of equilibrium dynamicsof quantum systems

C.16.1 Quantum out of equilibrium dy-namics (B. Sciolla, G. Biroli)

Signicant advances in the eld of ultra coldatoms have allowed one to engineer macroscopicquantum many-body systems in almost perfectisolation from the environment and probe theirout of equilibrium dynamics. In collaborationwith B. Sciolla [t10/123] we exactly solved theo-equilibrium dynamics of the innite dimen-sional Bose Hubbard Model after a quantumquench, which corresponds to a sudden changeof the repulsive interaction. This protocol andthis model are both relevant for experiments.For integer lling, we found a dynamical transi-tion separating regimes of small and large quan-tum quenches starting from the superuid state.This transition is very similar to the one foundfor the fermionic Hubbard model by mean eldapproximations. On a dierent front, motivatedby the studies of quantum non-equilibrium dy-namics induced by an external drive, we stud-ied the driven dynamics of quantum coarsening.In collaboration with C. Aron and L. Cuglian-dolo [t09/231, t10/270] we analyzed models ofM-component rotors coupled to two electronicreservoirs at dierent chemical potentials thatgenerate a current threading through the sys-tem. In the large M limit we derived the dy-namical phase diagram as a function of temper-ature, strength of quantum uctuations, voltageand coupling to the leads. We showed that theslow relaxation in the ordering phase is univer-sal. Our results should apply to generic drivenquantum coarsening. Finally, we studied thesymmetries of the generating functionals relatedto the dynamics of quantum and classical sys-tems. This allows a more deeper understandingof uctuation-dissipation relations and uctua-tion theorems out of equilibrium. The part onclassical dynamics has already been published in[t10/269].










C.16.2 Thermalization of isolated quan-tum systems (G. Biroli)

The thermalization for isolated quantum sys-tems after a sudden parameter change, a so-called quantum quench, is a question that re-cently received a lot of attention because of ex-periments in cold atoms. In collaboration withC. Kollath and A. Lauchli [t09/226] we inves-tigated the pre-requisites for thermalization fo-cusing on the statistical properties of the time-averaged density matrix and of the expectationvalues of observables in the nal eigenstates.We found that eigenstates, which are rare com-pared to the typical ones sampled by the micro-canonical distribution, are responsible for theabsence of thermalization of some innite inte-grable models and play an important role forsome non-integrable systems of nite size, suchas the Bose-Hubbard model. We claried theso called Eigenstate Thermalization Hypothesisand discussed two alternative scenarios for ther-malization. Moreover, in [t10/115] we analyzedthe statistical properties of the energy levelsof the extended one dimensional Bose Hubbardmodel and related them to thermalization andthe absence thereof found in previous DMRGanalyses.

C.16.3 Quantum phase space Brownianmotion, a simple open system (M.Bauer, D. Bernard)

The study of open quantum systems is alreadyquite old, but recent advances in quantum ma-nipulations of simple systems (photons, elec-trons, Q-bits) coupled to an environment haveled to a revival of interest. On a more mathe-matical side, these systems lead naturally in cer-tain limits to quantum versions of the standardclassical stochastic calculus. A missing ingredi-ent at the moment are stopping times.

In [t11/136] we present a detailed study ofa simple quantum stochastic process, the quan-tum phase space Brownian motion, which we ob-tain as the Markovian limit of a simple modelof an open quantum system: an harmonic os-cillator coupled linearly to a reservoir of har-monic oscillators, in such a way that the totalnumber operator is conserved. Taking a con-tinuous frequency distribution for the reservoirand going to a long time/small coupling limitleads to drastic simplications. This physicaldescription of the process allows us to specifyand to construct the dilation of the quantumdynamical maps, including conditional quantum

expectations. The quantum phase space Brown-ian motion possesses many properties similar tothose of the classical Brownian motion, notablyits increments are independent and identicallydistributed. Possible applications to dissipativephenomena in the quantum Hall eect are sug-gested. We also briey mention a proposal forthe notion of quantum stopping time and illus-trate it on a discrete time quantum evolution.

C.17 Quantum entanglement

C.17.1 Entanglement of two disjointintervals in a spin chain (V.Pasquier)

In collaboration with Shunsuke Furukawa andJun'ichi Shiraishi [t08/187] we have studied thegeneric scaling properties of the mutual infor-mation between two disjoint intervals, in a classof one-dimensional quantum critical systems de-scribed by the c=1 bosonic eld theory.1

A numerical analysis of a spin-chain modelreveals that the mutual information is scale-invariant and depends directly on the boson ra-dius. The results have been interpreted in termsof correlation functions of branch-point twistelds. This study has provided a new way to de-termine the boson radius, and furthermore hasdemonstrated the power of the mutual informa-tion to extract more rened information of con-formal eld theory than the central charge.

C.17.2 Entanglement in Rokhsar-Kivelson wave-functions andShannon entropy of spin chains(J.-M. Stéphan, G. Misguich, V.Pasquier)

The scaling of entanglement in two-dimensional(2d) quantum systems (massive or critical) is animportant theoretical question but the calcula-tions (numerical or analytical) are usually dif-cult if not impossible for a generic many-body Hamiltonian. In [t09/089] (collaborationwith S. Furukawa) it was realized that the calcu-lations simplify dramatically for a specic familyof wave-functions, dubbed Rokhsar-Kivelson.Such a 2d quantum state |ψ〉 is constructed froma 2d classical model of statistical mechanics (ex:Ising, vertex or hard-core dimer models) andthe weight ψ(c) of a classical conguration c issimply the (square root of) classical Boltzmannweight ψ(c) = exp(− 1

2E(c)). In some appro-priate geometry, the entanglement entropy ofa half-innite cylinder is then nothing but theShannon entropy S = −

∑i pi ln(pi) associated

1The mutual information IA,B of two subsystems A and B is dened as IA,B = SA + SB − SA∪B where SΩ isthe entanglement (Von-Neumann) entropy of the subsystem Ω.







to the (classical) probabilities pi to observe aconguration i at the frontier between the upperand lower half-innite cylinders. These pi canin turn be obtained from the dominant eigen-vector of the classical transfer matrix. This al-lowed to study the scaling of the entanglementin some RK states for relatively large 2d sys-tems. The dominant term is proportional to thelength of the boundary between the two subsys-tems but we identied a sub-leading and uni-versal constant to the entropy, which dependson the compactication radius for critical statescorresponding to a free boson. The 2d Ising uni-versality class was investigated in [t10/117].

In the picture above, the eigenvector of thetransfer matrix can be viewed as a 1d wave-function. Then, the ndings above lead us toconsider its Shannon entropy (and Rényi gener-alization) as a new probe for 1d quantum sys-tems. In [t10/225] the limit n =∞ or the Rényientropy was related to an entanglement measurein the case of the XXZ chain. In [t11/102] wefound a phase transition as a function of the ofthe Rényi parameter n, which was explained inCFT terms as a boundary phase transition andillustrated numerically on the XXZ and J1 − J2

chains.

C.17.3 Fidelity in critical spin chains (J.Dubail, J.-M. Stéphan, H. Saleur)

In recent years, it has been understood that en-tanglement measures are useful tools for the un-derstanding and characterization of new and ex-otic phases of matter, especially when the studyof local order parameters alone proves insu-cient. Among these measures, the entanglemententropy, dened through a bipartition of thequantum system, is the most established. In[t10/265] we introduce another quantity whichwe call bipartite delity for a generic quan-tum system. It is dened as the overlap be-tween its ground-state wave function, and theground-state one would obtain if the interactionsbetween two complementary subsystems wereswitched o. Although it is not strictly speakingan entanglement measure, we show that it enjoysseveral nice properties that are similar to theentanglement entropy. In particular, it allowsgenerically to detect quantum phase transition,and admits a universal scaling form ∼ (c/8) lnLat one-dimensional quantum critical points. Lis a typical size of the smallest subsystem andc is the central charge of the underlying confor-mal eld theory, describing the system at longdistances. We will also briey discuss otherpotential applications, for example to topolog-

ically ordered wave functions. In a related work[t08/246], Campos-Venuti, Saleur and Zanardihave studied the overlap of ground state wavefunctions of XXZ hamiltonians with dierentvalues of the anisotropy parameter, and sug-gested deep relations between the correspondingdelity and entanglement.

C.17.4 Entanglement spectrum in one-dimensional systems (A. Lefèvre)

Recent years have seen growing interest instudying quantum entanglement spectra. Atquantum critical points, they display remark-able scaling properties, which encode useful in-formation about correlations and the underly-ing symmetries. In addition, they are at thecore of algorithms using matrix product statessuch as DMRG, which compute truncated spec-tra in order to generate various observables. In[t08/265], we derived universal part of the con-tinuous spectrum of the reduced density matrixin one dimension, using a conformal eld the-ory method introduced by Calabrese and Cardy.The outcome of our calculation is perfectly inline with exact and numerical results obtainedfor XX and XXZ chains. Although this approachcannot provide the degeneracy of eigenvalues, itpredict accurately the gaps beetween them. Ourresults have been since widely used in order tointerpret numerical results from DMRG and de-sign precise convergence tests.

C.18 One-dimensional systems,quantum impurities andnanosystems

C.18.1 Transport out of equilbrium inthe IRLM (E. Boulat, H. Saleur)

Since 1995 ([t95/178]), Saleur and coworkershad proposed a strategy to compute out ofequilibrium transport properties in interactingquantum impurity problems by combining theBethe ansatz with a scattering description of the(open) systems. While in reasonable agreementwith experiments, their results had remainedthe subject of some controversy, in part becauseof the underlying integrability, which describestransport in terms of quasiparticles very dier-ent from the physical electrons. In the last fewyears, N. Andrei and collaborators had madethis criticism more acute in their (inconclusive)study of the interacting resonant level model(IRLM). In a series of works with E. Boulatand P. Schmitteckert, Saleur has revisited theissue. After extending the logic pioneered in[t95/178] to the IRLM in [t07/061], they man-








aged to calculate the current out of equilibriumanalytically and numerically in [t08/244]. Thenumerical calculation is intricate, and relies on asophisticated adaptation of the time dependentDMRG technique. Since the results of [t08/244]only hold in the universal eld theoretic limit,simulations have moreover to be performed ina wide range of values of microscopic parame-ters, in order to identify and validate the scal-ing region. The outcome entirely supported theanalytical results, hence validating the approachpioneered in [t95/178]. It was, in fact, one of thevery rst times where non equilibrium transportin the presence of interactions could be convinc-ingly tackled both numerically and analytically.

One of the fascinating features of this typeof quantum dot problem is the presence ofquaisparticles with a charge dierent from theelectron charge. This cannot be seen directlywhen studying the current, but becomes ob-servable when considering the zero tempera-ture shot noise, where, in the Poissonian limit,the Fano factor (noise/current) gives directlythe charge of the carriers. In [t10/116], Bran-schaedel, Boulat, Saleur and Schmitteckert onthe one hand managed to calculate the shot noisein closed form for the IRLM, on the other hand,managed to also determine this shot noise nu-merically, nding again excellent agreement be-tween the two approaches. The numerical cal-culation of the noise itself is of course consid-erably dicult, and relies on a straightforwardevaluation of time integral of two point func-tions of the current, together with a delicateanalysis of the nite size eect, as described in[t11/053]. Once again, the results are a rst, andjustify the astounding CPU time (above 2 mil-lion hours) spent on the project by the KarlsruheInstitute. Meanwhile, Saleur and coworkers havekept working [t07/202] on the determination ofthe full counting statistics, and have just man-aged to calculate it analytically for the problemof edge states tunneling in the fractional quan-tum Hall eect and the IRLM. The correspond-ing work will be published soon, and exhibitsmany relevant features, including a vericationof the Galavotti-Cohen identities.

C.18.2 Friedel oscillations in the Kondoeect (H. Saleur)

The length dependence of Kondo physics is muchless well understood than the temperature de-pendence. It is generally expected that physicalquantities exhibit a crossover at a length scaleroughly the inverse of the Kondo temperaturebut this crossover has never been observed ex-

perimentally and has sometimes been questionedtheoretically. One way of observing this lengthscale is through the density oscillations around amagnetic impurity. This idea has become partic-ularly timely due to possibility of scanning tun-neling microscopy of magnetic ions on metallicsurfaces.

Surprisingly, the literature on the subject ofcharge oscillations in the Kondo problem was al-most silent for many years. The origin is prob-ably the idea of spin-charge separation, whichsuggest that at low energy, all the physics is inthe spin sector, the charge sector being unaf-fected. This is not correct, but for slightly sub-tle reasons. The issue was fully claried by Af-eck, Borda and Saleur in [t08/108] who prop-erly identied the way to calculate the chargedensity in the scaling limit, performed pertur-bative analysis in the UV and IR, and also car-ried out numerical renormalization group calcu-lations.

C.18.3 Eects of interactions in carbonnanotubes (C. Bena)

The physics of one-dimensional systems such ascarbon nanotubes is believed to be dominatedby interactions, which lead to very strongly cor-related states of matter deemed Luttinger liq-uids. The main goal of our research in thiseld is to theoretically understand and modelquantities measurable in transport experiments,such as the conductance and the noise, as wellas the local density of states measurable in anSTM experiment. In particular, over the pastyears we have tried to understand how thesequantities, in particular the high-frequency non-symmetrized noise, are aected by the interplaybetween the strong electronic interactions andthe presence of metallic leads. Thus, with I.Sa (LPS Orsay) and A. Crepieux (CPT Mar-seille), we have computed the non-symmetrizednite-frequency noise in both FQHE edge states[t07/077] and in nanotubes [t08/153]. We wereamong the rst to study the eects of the inter-actions on the asymmetry in the nite-frequencynon-symmetrized noise, and we predicted thatthe fractionalization of charge in nanotubes canbe tested by such a measurement. Furthermore,in [t09/331], we have shown that the apparentlynon-interacting features observed by the groupof N. Mason (Urbana Champaign) in STM ex-periments performed with a superconducting tipdo not rule out the existence of strong interac-tions in carbon nanotubes.










C.18.4 Carbon nanotubes in contactwith superconductors (C. Bena)

Together with K. Le Hur (Yale) and S. Vishvesh-wara (UIUC) [t07/227], we have analyzed thedensity of states of a nanotube in contact witha superconducting substrate and we have foundthat an unconventional double-gap situation canarise in the two bands for nanotubes of largeradius: due to the interactions in the nan-otube, the appearance of a BCS gap in oneband of the nanotube stabilizes superconductiv-ity in the second band. Also, in collaborationto the Quantronics group in SPEC CEA Saclay,we have analyzed experimentally and theoreti-cally carbon nanotubes connected to supercon-ducting electrodes. These can carry a supercur-rent mainly transmitted by discrete entangledelectron-hole states conned to the nanotube,called Andreev bound states (ABS). In [t10/127]we have made the rst tunneling spectroscopyof individually resolved ABS. Also, by analyz-ing the evolution of the ABS spectrum with agate voltage and with magnetic ux, we haveshown that the ABS arise from the discrete elec-tronic levels of the molecule and that they re-veal detailed information about the energies ofthese levels, their relative spin orientation andthe coupling to the leads.

C.19 Anderson localization

C.19.1 Anderson model on Bethe lat-tices: density of states, local-ization properties and isolatedeigenvalue (G. Biroli)

In collaboration with G. Semerjian and M.Tarzia [t10/271], we revisited the Anderson lo-calization problem on Bethe lattices, putting incontact various aspects which have been previ-ously only discussed separately. For the case ofconnectivity 3 we compute by the cavity methodthe density of states and the evolution of the mo-bility edge with disorder. Furthermore, we showthat below a certain critical value of the disor-der the smallest eigenvalue remains delocalizedand separated by all the other (localized) onesby a gap. We also study the evolution of themobility edge at the center of the band with theconnectivity, and discuss the large connectivitylimit.

C.19.2 Anderson localization transitions(T. Garel, C. Monthus)

We have studied various aspects of Anderson lo-calization transitions. On the Cayley tree, An-derson localization can be analyzed in terms of

traveling waves and presents interesting analo-gies with the directed polymer model [t08/186,t11/020]. In dimension d = 2, 3, we haveused the exact Aoki renormalization procedure[t09/088]. An essential property of Andersonlocalization transitions is the multifractality ofeigenfunctions, as well as the multifractality oftwo-point Landauer transmission that we havestudied in various geometries [t09/051, t09/087,t09/155]. We have shown how some generalproperties of multifractal spectra could be ob-tained within a real-space renormalization anal-ysis: in [t09/177], we have analyzed the physi-cal origin of the exact symmetry of the multi-fractal spectrum in relation with the Gallavotti-Cohen uctuation relations of large deviationfunctions that are well-known in the eld of non-equilibrium dynamics; in [t10/069], we have ex-plained the statistics of critical Inverse Partici-pation Ratios in terms of the traveling-wave so-lutions of some appropriate renormalization pro-cedure. In [t10/136], we have developed a strongdisorder perturbation theory to better under-stand the strong multifractality regime; nallyin [t11/049], we have analyzed the exact renor-malization of the Dyson hierarchical model forAnderson localization. Besides these studies ofelectron localization, we have also characterizedthe localization properties of phonons in randomsystems [t10/080, t11/010].

C.19.3 Many body localization (T. Garel,C. Monthus)

The problem of many body localization can beseen as an Anderson localization problem in con-guration space. For a one-dimensional latticemodel of interacting fermions with disorder, wehave applied an exact renormalization proce-dure in conguration space to analyze the nite-disorder critical point [t10/043].

C.19.4 Spectral features and localiza-tion properties of simple quan-tum systems (J.-M. Luck)

The uctuations of the quantum conductancethrough a one-dimensional disordered systemconsisting of independent scattering units hasbeen investigated, in the regime where thelengths of the elementary units and their trans-mission probabilities are drawn independently,according to broad distributions. This modelse.g. the Anderson localization problem for anelectron in the presence of a non-stationary ran-dom potential whose uctuations grow with dis-tance. Four dierent phases have been charac-terized, depending on the values of the Lévy in-


















dices of both distributions: usual localization,underlocalization, superlocalization, and uctu-ating localization [t07/112].

We have analyzed the tight-binding elec-tronic spectra of various graphs with sphericaltopology, including the ve Platonic solids, thefullerene, and two families of polyhedra. Theeect of a quantized radial magnetic eld andthat of a radial electric eld in the presence ofstrong spin-orbit interactions have been stud-ied in parallel on the same structures. Mostof these spectra have been obtained analyticallyin closed form. They exhibit a rich pattern ofdegeneracies. This work has also revealed anunexpected correspondence between the mag-netic and electric problems at a special point[t08/003, t08/024].

The persistent currents and the magnetiza-tion of a multiply connected mesoscopic systemhave been explored in detail. The sample con-sists of two unequal clean metallic rings sharinga contact point, in a magnetic eld. Many novelfeatures with respect to the single-ring geome-try have been underlined, including the patternof twofold and threefold degeneracies, the keyrôle of length and ux commensurability, and inthe case of commensurate ring lengths the oc-currence of innitely many idle levels which donot carry any current [t08/202].

We have investigated the dynamical behav-ior of a quantum particle in low-dimensional sys-tems which are exceptions to the common wis-dom on localization, in the sense that the lo-calization length diverges at some isolated spe-cial energies. Two well-known one-dimensionalexamples have been dealt with in parallel:the chain with o-diagonal disorder and therandom-dimer model. The mean density proleof the particle becomes critical in the long-timeregime. The quantum motion exhibits a pecu-liar kind of anomalous diusion that we havedubbed bi-fractality [t11/009].

C.20 Bosonization in any dimen-sions and the Monte Carlosign fermion problem (C.Pépin)

In [t09/276, t10/015, t10/018], we derive a newbosonization method for a system of interact-ing fermions, working in any dimension. Themethod starts with a Hubbard-Stratonovich de-composition of the quartic interaction into acarefully chosen set of bosonic modes. The re-sulting eld theory is quadratic in the fermionicdegrees of freedom. We then write the equa-

tion of motion of the fermions self-consistentlyinteracting with the bosonic eld. Lastly thisequation of motion is re-exponentiated into thepartition function, using a technique standard inthe physics of stochastic equation : the Bechhi-Rouet-Stora-Tyupkin (BRST) technique. It in-volves extending the space of variables to a su-persymmetric version of it, with two additionalsupersymmetric parameters θ and θ, which ef-fectively reduce the dimension by two units.The resulting lagrangian is a ψ4-eld theory ofnon commutative but periodic in imaginary time[hence bosonic] elds ψ. We have started test-ing this new bosonization onto the old problemof re-summing the non analyticities of the Lan-dau Fermi liquid theory, and just recently got aresult [unpublished].

Meanwhile, we got interested in determiningwhether our new method of treating interact-ing fermions could be useful into bringing somenew light into the long standing Monte Carlosign fermion problem. The statistical errors inQuantum Monte Carlo (QMC) simulations arewell known to diverge for fermions in interac-tion. In these simulation techniques one evalu-ates the average 〈A〉 = Z−1

∑cA(c)p(c) where

p(c) is the probability of a specic congurationc, while Z =

∑c p(c). This technique is very

well suited to the evaluation of statistical aver-ages, as soon as p(c) is positive. But in the caseof a system of interacting fermions, p(c) is givenby a fermionic determinant, and can becomenegative for certain congurations of the inter-nal eld φ, where φ is, for example a Hubbard-Stratonovich eld introduced above. Our idea isto circumvent this problem within our bosoniza-tion method. Instead of re-exponentiating theequations of motion like in the analytic part, wewant to invert them numerically, after regular-izing them. The trick here is that since the wehave now written the equations of motion for abosonic eld [representing a particle-hole pair], aregularization is now possible, which eliminatesthe poles, hence all possibility of a singularity.Our solution is indeed positive for any congu-ration of the eld [absence of sign problem], andthe (QMC) codes converge quickly. We are cur-rently checking the convergence to the correctvalue, in the limit of large number of sites.

C.21 Open source libraries forstrongly correlated systems(O. Parcollet)

We participate to the development of opensources libraries for strongly correlated systemswithin the project ALPS 2.0 (Algorithms and










Libraries for Physics Simulations) [t11/084].

C.22 Polymers and polyelec-trolytes

The functionalization of surfaces by the adsorp-tion or grafting of polymers or polyelectrolytes isone of the most versatile and ecient techniquesto produce biomaterials or biosensors.

In the realm of the microelectronic indus-try, one of the big challenges is to nd aord-able ways of generating high-density orderednano-structures that can be transferred to a sil-icon substrate, in order to produce low cost mi-crochips. This can be done by adsorbing andordering lamellar phases of block copolymers onnano-patterned surfaces.

For both cases described above, the self-consistent eld theory is used to predict thephase diagrams, the polymer concentration, theion proles and other properties as a functionof the physical parameters. This should allow abetter control of the properties of the surface.

C.22.1 Block copolymer at nano-patterned surfaces (H. Orland)

In [t10/262], we present numerical calculationsof lamellar phases of block copolymers at pat-terned surfaces. We model symmetric diblockcopolymer lms forming lamellar phases andthe eect of geometrical and chemical sur-face patterning on the alignment and orienta-tion of lamellar phases. The calculations aredone within self-consistent eld theory (SCFT),where the semi-implicit relaxation scheme isused to solve the diusion equation. Two spe-cic set-ups, motivated by recent experiments,are investigated. In the rst, the lm is placedon top of a surface imprinted with long chemi-cal stripes. The stripes interact more favorablywith one of the two blocks and induce a perpen-dicular orientation in a large range of systemparameters. However, the system is found to besensitive to its initial conditions, and sometimesgets trapped into a metastable mixed state com-posed of domains in parallel and perpendicularorientations. In a second set-up, we study thelm structure and orientation when it is pressedagainst a hard grooved mold. The mold sur-face prefers one of the two components and thisset-up is found to be superior for inducing aperfect perpendicular lamellar orientation for awide range of system parameters.

C.22.2 Organization of block copolymersusing NanoImprint lithography:comparison of theory and exper-iments (H. Orland)

In [t11/090], we present NanoImprint lithog-raphy experiments and modeling of thin lmsof block copolymers (BCP). The NanoImprinttechnique is found to be an ecient tool notonly to align lamellar phases perpendicularly tothe substrate, but also to get rid of in-plane de-fects over distances much larger than the nat-ural lamellar periodicity. The modeling relieson self-consistent eld calculations done in two-and three-dimensions, and is found to be in goodagreement with the experiments. It also oerssome insight on the NanoImprint lithographysetup and on the conditions required to perfectlyordered BCP lamellae.

C.23 Coulombic systems

Electrostatics is one of the main driving forcesin biological systems. In particular, the or-ganization of ions and water around chargedbiomolecules substantially determines their in-and out-of-equilibrium biochemical properties.The mean-eld Poisson-Boltzmann theory hasbeen successfully applied to biological systems.However, it lacks two important ingredients: i)the discreteness of water, which in rst approxi-mation can be viewed as permanent dipoles, andii) the nite size of ions and of water molecules.The works in this section deal with includingthese two eects, namely dipolar water and -nite sizes of ions and water, by suitably mod-ifying the Poisson-Boltzmann equations. Thisgeneralized theory is applied to the solvation ofproteins or small molecules in water.

C.23.1 Incorporating dipolar solventswith variable density in Poisson-Boltzmann electrostatics (M. Bon,H. Orland)

We describe a new way to calculate the elec-trostatic properties of macromolecules that goesbeyond the classical Poisson-Boltzmann treat-ment with only a small extra CPU cost. Thesolvent region is no longer modeled as a ho-mogeneous dielectric media but rather as anassembly of self-orienting interacting dipoles ofvariable density. The method eectively uniesboth the Poisson-centric view and the LangevinDipole model. The model results in a variabledielectric constant ε(r) in the solvent region andalso in a variable solvent density ρ(r) that de-pends on the nature of the closest exposed so-lute atoms. The model was calibrated using





small molecules and ions solvation data withonly two adjustable parameters, namely the sizeand dipolar moment of the solvent. Hydropho-bicity scales derived from the solvent densityproles agree very well with independently de-rived hydrophobicity scales, both at the atomicor residue level. Dimerization interfaces in ho-modimeric proteins or lipid-binding regions inmembrane proteins clearly appear as poorly sol-vated patches on the solute accessible surface.Comparison of the thermally averaged solventdensity of this model with the one derived frommolecular dynamics simulations shows qualita-tive agreement on a coarse-grained level. Be-cause this calculation is much more rapid thanthat from molecular dynamics, applications ofa density-prole-based solvation energy to theidentication of the true structure among a setof decoys become computationally feasible. Var-ious possible improvements of the model are dis-cussed, as well as extensions of the formalismto treat mixtures of dipolar solvents of dierentsizes.[t08/286]

C.23.2 Solvation of ion pairs: thePoisson-Langevin model (H. Or-land)

Salt bridges play an important role in proteinstability and protein-protein interactions. Wehave computed the electrostatics free energiesof analogues of charged amino acid sidechainsusing two dierent implicit solvent models, thePoisson-Boltzmann (PB) model and our ownPoisson-Langevin (PL) model, and comparedtheir values to results from explicit solvent freeenergy calculations. A systematic dierence isobserved between the PB and explicit results,which we attribute to the basic assumption ofPB that water density is constant. In contrast,the PL results match remarkably well with theexplicit solvent results. We attribute this successto the ability of the PL model to give a realisticpicture of the dielectric response of water to thepresence of charged molecules.[t09/333]

C.23.3 Computing ion solvation free en-ergies using the dipolar Poissonmodel (H. Orland)

A new continuum model is presented for com-puting the solvation free energies of cationsin water. It combines in a single formalismbased on statistical thermodynamics the Pois-son model for electrostatics with the Langevindipole model to account for nonuniform waterdipole distribution around the ions. An excel-lent match between experimental and computed

solvation free energies is obtained for 10 mono-valent and divalent ions.[t09/312]

C.23.4 Beyond the Poisson-Boltzmannmodel: modeling biomolecule-water and water-water interac-tions (H. Orland)

We present an extension to the Poisson-Boltzmann model in which the solvent is mod-eled as an assembly of self-orienting dipoles ofvariable densities. Interactions between thesedipoles are included implicitly using a Yukawapotential eld. This model leads to a set ofequations whose solutions give the dipole den-sities; we use the latter to study the organiza-tion of water around biomolecules. The com-puted water density proles resemble those de-rived from molecular dynamics simulations. Wealso derive an excess free energy that discrim-inates correct from incorrect conformations ofproteins.[t09/311]

C.24 Physics of DNA: theoreticaland experimental investiga-tions

DNA, the carrier of genetic information, is em-bedded in polymerized nucleic acids, and asa result, many topics of the molecular biol-ogy of gene raise fundamental issues of polymerphysics, for instance in DNA condensation, inthe interaction of DNA with surfaces, in DNAhybridization and in DNA translocation throughmembranes.

C.24.1 Aggregation and adsorption atthe air-water interface of bac-teriophage phi X174 single-stranded DNA (J.-L. Sikorav)

Chromosomal DNA molecules are in condensedstates in cells, corresponding to a chain con-formation much denser than that of a randomcoil state. A central issue in molecular biol-ogy is to understand the consequences of DNAcondensation on fundamental processes such asDNA replication or gene expression. We havediscovered a coupling between the processes ofDNA condensation (here an aggregation in thebulk of the solution) and DNA adsorption atthe air-water interface, thus establishing a linkbetween the previously disconnected elds ofDNA condensation and of surface science ofDNA.[t08/305]

C.24.2 DNA adsorption at liquid/solidinterfaces (J.-L. Sikorav)

We have characterized DNA adsorption ata liquid/solid interface by X-ray reectivity.







Monodisperse double-stranded DNA moleculeswere adsorbed on a positively charged surface,obtained through chemical grafting of a homo-geneous organic monomolecular on an oxide-freemonocrystalline Si(111) wafer. The adsorbedDNA is found to incrust into the soft mono-layer. The surface coverage is very high, andthe adsorbed layer is expected to display 2D ne-matic ordering. This system is promising for thedevelopment of nucleic acid chip hybridizationtechnologies.[t08/304]

C.24.3 Mechanism of thermal renatura-tion and hybridization of nucleicacids: Kramers' process and uni-versality in Watson-Crick basepairing (H. Orland, J.-L. Sikorav)

The hybridization of complementary single-strands nucleic acids is involved in essential bio-logical processes (such as genetic recombination)and is the most important tool of biotechnologies(through Polymerase Chain Reaction or PCR,DNA chips . . . ). The understanding of its mech-anism is therefore a subject of fundamental andapplied interest. Yet, more than fty years aftertheir discovery, hybridization reactions remainpoorly understood. They have been described intwo types of experimental conditions: initially insimple homogeneous systems, and later in a va-riety of heterogeneous systems, in which the re-acting chains undergo a phase separation (suchas an aggregation or an adsorption) concomi-tant with the reaction. We have investigated themechanism of hybridization in simple, homoge-neous conditions, where the rate of the reactionis known to increase as a power law of the av-erage degree of polymerization of the reactingsingle-strands. We have found that the reactionis not diusion controlled (as believed earlier),but instead is an activated process that can bedescribed with Kramers' rate theory. The re-acting single-strands are in universal good sol-vent conditions. The length dependence of therate results from a thermodynamic excluded vol-ume eect. The scaling exponent is determinedby an equilibrium monomer contact probability,which involves a critical exponent described bydes Cloizeaux. The predicted value for this ex-ponent (0.52 ± 0.01) agrees closely with the ex-perimental results (0.51 ± 0.01). The rate of thehybridization can be considerably increased inheterogeneous systems, up to one million fold,and our work should contribute to clarify themechanisms involved.[t08/284]

C.24.4 A model for polymer transloca-tion (K. Mallick)

In [t10/063], we investigate a model ofchaperone-assisted polymer translocationthrough a nanopore in a membrane. Transloca-tion is driven by irreversible random sequentialabsorption of chaperone proteins that bind tothe polymer on one side of the membrane. Theproteins are larger than the pore and hence thebackward motion of the polymer is inhibited.This mechanism recties Brownian uctuationsand results in an eective force that drags thepolymer in a preferred direction. The translo-cated polymer undergoes an eective biasedrandom walk and we compute the correspond-ing diusion constant. Our methods allow usto determine the large deviation function which,in addition to velocity and diusion constant,contains the entire statistics of the translocatedlength.

C.25 Statistical physics of ho-mopolymeric RNA

Thermodynamic experiments, such as melting orpulling on RNA, allow to measure, or at leastassess, some physical parameters necessary toparametrize their free energy function. In thissection, we present some work on the thermody-namics of homo-RNA, in particular the determi-nation of the loop exponents.

C.25.1 Impact of loop statistics on thethermodynamics of RNA folding(H. Orland)

Loops are abundant in native RNA structuresand proliferate close to the unfolding transition.By including a statistical weight l−c for loopsof length l in the recursion relation for the par-tition function, we show that the heat capacitydepends sensitively on the presence and value ofthe exponent c, even for a short explicit tRNAsequence. For long homo-RNA we analyticallycalculate the critical temperature and criticalexponents which exhibit a non-universal depen-dence on c. [t08/049]

C.25.2 Secondary structure formation ofhomopolymeric single-strandednucleic acids including force andloop entropy: implications forDNA hybridization (H. Orland)

Loops are essential secondary structure elementsin folded DNA and RNA molecules and prolifer-ate close to the melting transition. Using a the-ory for nucleic acid secondary structures thataccounts for the logarithmic entropy −c logm






for a loop of length m, we study homopoly-meric single-stranded nucleic acid chains underexternal force and varying temperature. In thethermodynamic limit of a long strand, the chaindisplays a phase transition between a low tem-perature / low force compact (folded) structureand a high temperature / high force molten (un-folded) structure. The inuence of c on phasediagrams, critical exponents, melting, and forceextension curves is derived analytically. For van-ishing pulling force, only for the limited rangeof loop exponents 2 < c < 2.479 a melting tran-sition is possible; for c≤2 the chain is alwaysin the folded phase and for 2.479 < c alwaysin the unfolded phase. A force induced melt-ing transition with singular behavior is possiblefor all loop exponents c < 2.479 and can be ob-served experimentally by single molecule forcespectroscopy. These ndings have implicationsfor the hybridization or denaturation of doublestranded nucleic acids. The Poland-Scheragamodel for nucleic acid duplex melting does notallow base pairing between nucleotides on thesame strand in denatured regions of the doublestrand. If the sequence allows these intra-strandbase pairs, we show that for a realistic loop ex-ponent c ≈ 2.1 pronounced secondary structuresappear inside the single strands. This leads toa lower melting temperature of the duplex thanpredicted by the Poland-Scheraga model. Fur-ther, these secondary structures renormalize theeective loop exponent c, which characterizesthe weight of a denatured region of the doublestrand, and thus aect universal aspects of theduplex melting transition.[t11/092]

C.26 Statistical physics of randomRNA

Random RNA is studied, in particular in orderto shed some light on the expected glass transi-tion at low temperature.

F. David has been interested in the problemof the secondary structure of long RNA strands(m-RNA for instance) and the role of base disor-der on the secondary structure. Unlike proteinfolding, which exhibits a strong interdependencebetween secondary and tertiary structure, RNAfolding may be studied at the level of secondarystructures due to a clear separation of energyscales. Since the pioneering work of Bundschuhand Hwa, several authors have studied the sta-tistical physics of RNA secondary structures forrandom sequences, in particular at IPhT. It iscommonly believed that these systems undergoa freezing transition upon lowering the temper-ature.

The nature of the freezing transition and theproperties of the low temperature/strong dis-order glassy phase was still poorly understood,even at the level of statics. In particular topo-logical constraints (planarity) induce frustrationand compete with long range forces. This istherefore a dicult and fascinating problem atthe interface between the physics ( and themathematics) of disordered systems, and quan-titative biology.

C.26.1 Field theory for random RNA (F.David)

The program initiated by F. David and KayWiese (École Normale Supérieure) in 2005 (toformulate a systematic and consistent eldtheory for Random RNA folding) has beenachieved. This program is based on an ensembleof new tools: formulation of the model in termsof random walks in an auxiliary D = 3 dimen-sional space, introduction of random-matrix-likeauxiliary elds to implement topological con-straints, and the use of a multilocal operatorproduct expansion to analyse the UV and IRdivergences of the model.

In a long and thorough article the denitionof the model is detailed. This eld theory isshown to be renormalizable to all orders in per-turbation theory in D = 2 + ε. This establishesthe consistency of the calculation at rst orderin ε of Lässig-Wiese. Moreover the renormaliz-ability allows to work in the new (and simpler)scheme of open polymers, which was alreadyused by F.D. and K.W. to study denaturationof random RNA under tension. The scaling ex-ponents of the model at the freezing transitionare computed for the rst time at 2-loop order.Exact scaling identities between exponents areproven. The systematic treatment of the denat-uration transition of random RNA is also pre-sented for the rst time, as well as 2 loop calcu-lations for the critical exponents for this transi-tion. Finally the relevance of the model and ofthese calculations for the understanding of thelow temperature glassy phase of random RNA isdiscussed.[t09/074]

C.26.2 A growth model for randomRNA (F. David)

Together with C. Hagendorf and K. J. Wiese(École Normale Supérieure), F. David has in-troduced a new non perturbative formulation ofrandom RNA folding based on hierarchical ap-proximations. This hierarchical model is shownto be equivalent to a tree-growth model withsome special properties, and also to some frag-




mentation model. Both models can be solvedanalytically, giving access to exact scaling ex-ponents and fractal dimensions, to scaling func-tions for large molecules, and to the correctionsto scaling (which is new for these kind of mod-els). These results are checked by numerical sim-ulations of up to 6500 bases. The equivalence ofRNA models with growth/fragmentation modelsshould be helpful in understanding more generaltree-growth processes.[t07/068]

C.27 Pseudoknot prediction in bi-ological RNA

In the last fteen years, it has been recognizedthat RNA is a major actor in the biology of thecell, not only as an information carrier, but alsobecause of its enzymatic and regulatory action.The biological activity of RNA is closely relatedto its folded structure.

The simplicity of the RNA secondary struc-ture problem makes the enumeration of sec-ondary structures a classic combinatorics prob-lem. This aspect has been tackled by randommatrix theory, and in the case of random RNA,by simplied hierarchichal models.

For real RNA biological data, a classicationof RNA pseudoknots according to their genus isproposed. With this classication, it is shownthat RNA of size smaller than 500 bases havevery low genus (< 3) and this allows to generateecient algorithms for the prediction of RNAstructures.

C.27.1 Prediction of RNA secondarystructures with pseudoknots (M.Bon, H. Orland)

We present a new algorithm to predict RNAsecondary structures with pseudoknots. Themethod is based on a classication of RNA struc-tures according to their topological genus. Thealgorithm utilizes a simplied parametrizationof the free energies for pair stacking, loop penal-ties, etc. and in addition a free energy penaltyproportional to the topological genus of the pair-ing graph. Our method can take into accountall pseudoknot topologies and achieves high suc-cess rates compared to state-of-the-art methods.This shows that the genus is a promising conceptto classify pseudoknots.[t10/261]

C.27.2 TT2NE: a novel algorithm topredict RNA secondary struc-tures with pseudoknots (M. Bon,H. Orland)

We present TT2NE, a new algorithm to predictRNA secondary structures with pseudoknots.

The method is based on a classication of RNAstructures according to their topological genus.TT2NE guarantees to nd the minimum freeenergy structure irrespectively of pseudoknottopology. This unique prociency is obtainedat the expense of the maximum length of se-quence that can be treated but comparison withstate-of-the-art algorithms shows that TT2NE isa very powerful tool within its limits. Analysisof TT2NE's wrong predictions sheds light on theneed to study how sterical constraints limit therange of pseudoknotted structures that can beformed from a given sequence. An implementa-tion of TT2NE on a public server can be foundat http://ipht.cea.fr/rna/tt2ne.php. [t11/089]

C.27.3 Random matrix theory and RNAfolding (H. Orland)

In this article we review a series of recent ap-plications of random matrix theory (RMT) tothe problem of RNA folding. The intimate con-nection between these two elds of study liesin their common diagrammatic description: allsecondary structures of an RNA molecule arerepresented by planar diagrams which are nat-urally interpreted as the Feynman diagrams ofa suitable large-N matrix model. As a conse-quence, all subleading 1/N corrections of the ma-trix model correspond to diagrams that are notplanar, and that can be mapped into folded con-gurations of the RNA molecule including pseu-doknots. Moreover, the standard topological ex-pansion of the matrix model induces an elegantclassication of all possible RNA pseudoknots,according to their topological genus. The RMT-based statistical description of the RNA-foldingproblem has been extended also to the folding ofa generic homopolymer with saturating interac-tion. While reviewing several known ndings,we extend previous results about the asymp-totic distribution of pseudoknots of a phantomhomopolymer chain in the limit of large chainlength.[t11/088]

C.28 Dynamics of protein folding

This section addresses the problem of the de-termination of transition paths in protein fold-ing. The question can be formulated as fol-lows: which are the paths connecting a dena-tured state of a protein to its native state? Thisproblem is studied with the use of path inte-grals, which sum the possible trajectories of theprotein in conformation space, weighted by theircorrect action. This path-integral is then evalu-ated by the saddle-point method, which exhibitsthe dominant path. Fluctuations can be com-



http://ipht.cea.fr/rna/tt2ne.php




puted and the method is illustrated on variousexamples, both with classical or quantum forceelds.

C.28.1 Dominant reaction pathways inhigh dimensional systems (H. Or-land)

This paper is devoted to the development of atheoretical and computational framework to ef-ciently sample the statistically signicant ther-mally activated reaction pathways, in multi-dimensional systems obeying Langevin dynam-ics. We show how to obtain the set of most prob-able reaction pathways and compute the cor-rections due to quadratic thermal uctuationsaround such trajectories. We discuss how toobtain predictions for the evolution of arbitraryobservables and how to generate conformationswhich are representative of the transition stateensemble. We present an illustrative implemen-tation of our method by studying the diusionof a point particle in a 2-dimensional funneledexternal potential.[t08/283]

C.28.2 Kramers theory for conforma-tional transitions of macro-molecules (H. Orland)

We consider the application of Kramers theoryto the microscopic calculation of rates of con-formational transitions of macromolecules. Themain diculty in such an approach is to lo-cate the transition state in a huge congurationspace. We present a method which identies thetransition state along the most probable reactionpathway. It is then possible to microscopicallycompute the activation energy, the damping co-ecient, the eigenfrequencies at the transitionstate and obtain the rate, without any a-priorichoice of a reaction coordinate. Our theoreticalresults are tested against the results of Molec-ular Dynamics simulations for transitions in a2-dimensional double well and for the cis-transisomerization of a linear molecule.[t08/282]

C.28.3 Stochastic dynamics and domi-nant protein folding pathways (H.Orland)

We present the results of a recently developedtheoretical framework denominated DominantReaction Pathways (DRP), to study thermallyactivated reactions in multi-dimensional sys-tems. In particular, we focus on applicationto the protein folding reaction. By applyingthe saddle-point approximation to the stochasticpath integral generated by the Langevin equa-tion, we derive a least-action principle, whichallows us to rigorously determine directly the

most probable reaction pathways, bypassing thelong-standing computational problems associ-ated with the decoupling of time-scales in theproblem. We show the results of number val-idation studies, in which the accuracy of theDRP approach was assessed, studying molec-ular transitions. In all cases, the DRP pre-dictions are found to be consistent with theMD results, but extremely less computationallyexpensive.[t08/287]

C.28.4 Simulating stochastic dynamicsusing large time steps (H. Orland)

We present a novel approach to investigatethe long-time stochastic dynamics of multi-dimensional classical systems, in contact with aheat-bath. When the potential energy landscapeis rugged, the kinetics displays a decoupling ofshort and long time scales and both MolecularDynamics (MD) or Monte Carlo (MC) simula-tions are generally inecient. Using a eld theo-retic approach, we perform analytically the aver-age over the short-time stochastic uctuations.This way, we obtain an eective theory, whichgenerates the same long-time dynamics of theoriginal theory, but has a lower time resolutionpower. Such an approach is used to develop animproved version of the MC algorithm, which isparticularly suitable to investigate the dynamicsof rare conformational transitions. In the spe-cic case of molecular systems at room temper-ature, we show that elementary integration timesteps used to simulate the eective theory canbe chosen a factor ∼ 100 larger than those usedin the original theory. Our results are illustratedand tested on a simple system, characterized bya rugged energy landscape.[t09/306]

C.28.5 Dominant reaction pathways inprotein folding: a direct valida-tion against molecular dynamicssimulations (H. Orland)

The dominant reaction pathway (DRP) is analgorithm to microscopically compute the mostprobable reaction pathways in the overdampedLangevin dynamics without investing computa-tional time in simulating the local thermal mo-tion in the metastable congurations. In orderto test the accuracy of such a method, we in-vestigate the dynamics of the folding of a betahairpin within a model that accounts for bothnative and non-native interactions. We comparethe most probable folding pathways calculatedwith the DRP method with the folding trajecto-ries obtained directly from molecular dynamicssimulations. We nd that the two approaches






give consistent results.[t09/305]

C.28.6 Dominant folding pathways ofa peptide chain, from ab-initioquantum-mechanical simulations(H. Orland)

Using the Dominant Reaction Pathwaysmethod, we perform an ab-initio quantum-mechanical simulation of a conformational tran-sition of a peptide chain. The method we pro-pose makes it possible to investigate the out-of-equilibrium dynamics of these systems, withoutresorting to an empirical representation of themolecular force eld. It also allows to studyrare transitions involving rearrangements in theelectronic structure. By comparing the resultsof the ab-initio simulation with those obtainedemploying a standard force eld, we discuss itscapability to describe the non-equilibrium dy-namics of conformational transitions.[t10/124]

C.28.7 Fluctuations in the ensemble ofreaction pathways (H. Orland)

The dominant reaction pathway (DRP) is a rig-orous framework to microscopically compute themost probable trajectories, in non-equilibriumtransitions. In the low-temperature regime,such dominant pathways encode the informa-tion about the reaction mechanism and can beused to estimate non-equilibrium averages of ar-bitrary observables. On the other hand, at suf-ciently high temperatures, the stochastic uc-tuations around the dominant paths become im-portant and have to be taken into account. Inthis work, we develop a technique to systemat-ically include the eects of such stochastic uc-tuations, to order kBT . This method is used tocompute the probability for a transition to takeplace through a specic reaction channel and toevaluate the reaction rate.[t10/264]

C.28.8 Generating transition paths byLangevin bridges (H. Orland)

We propose a novel stochastic method to gener-ate paths conditioned to start in an initial stateand end in a given nal state during a certaintime tf . These paths are weighted with a prob-ability given by the overdamped Langevin dy-namics. We show that these paths can be ex-actly generated by a non-local stochastic dier-ential equation. In the limit of short times, weshow that this complicated non-solvable equa-tion can be simplied into an approximate lo-cal stochastic dierential equation. For longertimes, the paths generated by this approximateequation do not satisfy the correct statistics, butthis can be corrected by an adequate reweight-

ing of the trajectories. In all cases, the pathsare statistically independent and provide a rep-resentative sample of transition paths. Themethod is illustrated on the one-dimensionalquartic oscillator.[t11/091]

C.29 Molecular motors and dy-namics of actin laments

C.29.1 Molecular spiders (K. Mallick)

In recent years, chemists have constructed spec-tacular synthetic molecular systems which canmove on surfaces and tracks. One such ob-ject is a multi-pedal molecular spider whoselegs are short single-stranded segments of DNA.These spiders can move on a surface coveredwith single-stranded DNA segments, called sub-strates. The substrate DNA is complementaryto the leg DNA. The motion proceeds as legsbind to the surface DNA through the Watson-Crick mechanism, then dissociate, then rebindagain, etc. More precisely, a bond on the sub-strate with an attached leg is rst cleaved, andthe leg then dissociates from the aected sub-strate (which we shall call product). After thatthe leg can rebind to the new substrate or to theproduct.

In [t07/182], we establish dierent mappingsbetween various models of spiders and simple ex-clusion processes. This allows us to classify dif-ferent type of models and to select exactly solv-able cases as templates. For spiders with simplegait and varying number of legs, this allows usto compute the diusion coecient and, whenthe hopping is biased, their velocity.

C.29.2 Fluctuation relations and molec-ular motors (K. Mallick)

Motor proteins are nano-machines that con-vert chemical energy into mechanical work andmotion. Important examples include kinesin,myosin, and RNA polymerase. Despite a num-ber of theoretical models, understanding themechanochemical transduction mechanisms be-hind these motors remains a signicant chal-lenge: indeed, such systems are far from equilib-rium and display large uctuations. Thus, theusual framework of equilibrium statistical me-chanics can not be applied.

In [t07/183], we investigate theoretically theviolations of Einstein and Onsager relations, andthe eciency for a single processive motor oper-ating far from equilibrium using an extensionof the discrete two-state motor model. Withthe aid of the Fluctuation Theorem, we ana-lyze the general features of these violations andthis eciency and link them to mechanochemi-








cal couplings of motors. In particular, an anal-ysis of the experimental data of kinesin usingour framework leads to interesting predictionsthat may serve as a guide for future experiments.In [t08/210], we study a ashing ratchet modelwith switching between two continuous poten-tials. We show that this model exhibits theGallavotti-Cohen symmetry relation, providedthat the dynamics is described in terms of achemical and a mechanical variable. The sym-metry is obeyed by the generating function ofthe mechano-chemical currents. This function,which contains all the long time properties ofthe currents, can be determined exactly in somesimple cases. We review the relations betweenmodels of molecular motors and uctuation the-orems in [t09/246].

C.29.3 Dynamics of lament growth andinstabilities (K. Mallick)

A large number of structural elements of cellsare made of bers. Well studied examples ofthese bers are microtubules and actin la-ments. Microtubules are able to undergo rapiddynamic transitions between growth (polymer-ization) and decay (depolymerization) in a pro-cess called dynamic instability. Actin lamentsare able to undergo treadmilling-like motion.These dynamic features of microtubules andactin laments play an essential role in cellu-lar biology. For instance, the treadmilling ofactin laments occurs in lopodia, lamellipodia,agella and stereocilia. Actin growth dynamicsis also important in acrosome reactions, wheresperm fuses with egg. During cell division, themovements of chromosomes are coupled to theelongation and shortening of the microtubules towhich they bind.

In [t08/207], we study the stochastic dynam-ics of growth and shrinkage of single actin la-ments or microtubules taking into account in-sertion, removal, and ATP/GTP hydrolysis ofsubunits. The resulting phase diagram containsthree dierent phases: a rapidly growing phase,an intermediate phase and a bound phase. Weanalyze all these phases, with an emphasis onthe bound phase. We also discuss how hydrolysisaects force-velocity curves. The bound phaseshows features of dynamic instability, which wecharacterize in terms of the time needed for theATP/GTP cap to disappear as well as the timeneeded for the lament to reach a length of zero(i.e. to collapse) for the rst time. We ob-tain exact expressions for all these quantities,which we test using Monte Carlo simulations. In[t09/247], we extend this approach in two ways

by including the dynamics of both ends and bycomparing two possible mechanisms of ATP hy-drolysis. Our emphasis is mainly on two possiblelimiting models for the mechanism of hydrolysiswithin a single lament, namely the vectorial orthe random model. We propose a set of exper-iments to test the nature of the precise mech-anism of hydrolysis within actin laments. In[t10/218], we develop a model to describe theforce generated by an array of well-separatedparallel biolaments, such as actin laments.The N laments are assumed to only be coupledthrough mechanical contact with a movable bar-rier. We calculate the lament density distribu-tion and the force-velocity relation with a mean-eld approach combined with simulations. Weidentify two regimes: a non-condensed regimeat low force in which laments are spread outspatially, and a condensed regime at high forcein which laments accumulate near the barrier.We conrm that in this model, the stall force isequal to N times the stall force of a single l-ament. However, surprisingly, for large N , wend that the velocity approaches zero at forcessignicantly lower than the stall force.

C.30 Bioinformatics

Bioinformatics provide tools to analyze and or-ganize biological data. Two of the emblematicproblems of bioinformatics are studied in thissection, namely sequence alignment and struc-ture alignment. In both cases, sophisticatedmethods from statistical physics are used to pro-pose a solution to these problems. The algo-rithm for structural alignment is then used tostudy and classify knots in proteins.

C.30.1 Bernoulli matching model andsequence alignment (K. Mallick)

The goal of a sequence alignment problem isto nd similarities in patterns in dierent se-quences. Sequence alignment is one of themost useful quantitative methods of evolution-ary molecular biology. A classic alignment prob-lem deals with the search of the Longest Com-mon Subsequence (LCS) in two random se-quences. Finding analytically the statistics ofLCS of a pair of sequences randomly drawn fromthe alphabet of c letters is a challenging prob-lem in computational evolutionary biology. Theexact asymptotic results for the distribution ofLCS have been derived recently in in a sim-pler, yet nontrivial, variant called the BernoulliMatching model.

In [t07/169], we apply the Bethe ansatz tech-nique to the Bernoulli Matching model via an ex-








act mapping to the 5-vertex model on a squarelattice. Considering the terrace-like representa-tion of the sequence alignment problem, we re-produce by the Bethe ansatz the results for theaveraged length of the Longest Common Subse-quence in Bernoulli approximation. In addition,we compute the average number of nucleationcenters of the terraces.

C.30.2 MISTRAL: a tool for energy-based multiple structural align-ment of proteins (H. Orland)

The steady growth of the number of availableprotein structures has constantly motivated thedevelopment of new algorithms for detectingstructural correspondences in proteins. Detect-ing structural equivalences in two or more pro-teins is computationally demanding as it typi-cally entails the exploration of the combinato-rial space of all possible amino acid pairings inthe parent proteins. The search is often aidedby the introduction of various constraints suchas considering protein fragments, rather thansingle amino acids, and/or seeking only sequen-tial correspondences in the given proteins. Anadditional challenge is represented by the di-culty of associating to a given alignment, a re-liable a priori measure of its statistical signi-cance. Results: Here, we present and discussMISTRAL (Multiple STRuctural ALignment),a novel strategy for multiple protein alignmentbased on the minimization of an energy func-tion over the low-dimensional space of the rela-tive rotations and translations of the molecules.The energy minimization avoids combinatorialsearches and returns pairwise alignment scoresfor which a reliable a priori statistical signi-cance can be given.[t09/313]

C.30.3 Knotted vs. unknotted proteins:evidence of knot-promoting loops(H. Orland)

Knotted proteins, because of their ability tofold reversibly in the same topologically en-tangled conformation, are the object of an in-creasing number of experimental and theoret-ical studies. The aim of the present investi-gation is to assess, on the basis of presentlyavailable structural data, the extent to whichknotted proteins are isolated instances in se-quence or structure space, and to use compara-tive schemes to understand whether specic pro-tein segments can be associated to the occur-rence of a knot in the native state. A signi-cant sequence homology is found among a siz-able group of knotted and unknotted proteins.

In this family, knotted members occupy a pri-mary sub-branch of the phylogenetic tree anddier from unknotted ones only by additionalloop segments. These knot-promoting loops,whose virtual bridging eliminates the knot, arefound in various types of knotted proteins. Valu-able insight into how knots form, or are encoded,in proteins could be obtained by targeting theseregions in future computational studies or exci-sion experiments.[t10/263]

C.30.4 Mistral WebServer (H. Orland)

http://ipht.cea.fr/protein.php

C.30.5 TT2NE WebServer (H. Orland)

http://ipht.cea.fr/tt2ne.php

Bibliography[t07/068] F. David, C. Hagendorf, and K.J.

Wiese. A growth model for RNA sec-ondary structures. J. Stat. Mech., P04008,(2008), arXiv:0711.3421.

[t07/070] J. Bouttier, M.J. Bowick, E. Guitter,and M. Jeng. Vacancy localization in thesquare dimer model. Phys. Rev. E, 76,041140, (2007), arXiv:0706.1016.

[t07/112] D. Boosé and J.M. Luck. Statisticsof quantum transmission in one dimen-sion with broad disorder. J. Phys. A, 40,1404514067, (2007), arXiv:0708.0761.

[t07/128] C. Toninelli and G. Biroli. A NewClass of Cellular Automata with a Discon-tinuous Glass Transition. J. Stat. Phys.,130, 83112, (2008), arXiv:0709.0378.

[t07/130] C. Monthus and T. Garel. Criti-cal points of quadratic renormalizationsof random variables and phase transitionsof disordered polymer models on diamondlattices. Phys. Rev. E, 77, 021132, (2008),arXiv:0710.0735.

[t07/133] C. Monthus and T. Garel. Disorder-dominated phases of random systems : re-lations between tails exponents and scal-ing exponents. J. Stat. Mech., P01008,(2008), arXiv:0710.2198.

[t07/147] T. Aspelmeier, A. Billoire, E. Mari-nari, and M.A. Moore. Finite size cor-rections in the Sherrington-Kirkpatrickmodel. J. Phys. A, 41, 324008, (2008),arXiv:0711.3445.

[t07/152] C. Monthus and T. Garel. Criticalbehavior of interfaces in disordered Potts



http://ipht.cea.fr/protein.php

http://ipht.cea.fr/tt2ne.php










ferromagnets : statistics of free-energy, en-ergy and interfacial adsorption. Phys. Rev.B, 77, 134416, (2008), arXiv:0711.2878.

[t07/159] G. Misguich and F. Mila. Quan-tum Dimer Model on the triangular lat-tice: Semiclassical and variational ap-proaches to vison dispersion and conden-sation. Phys. Rev. B, 77, 134421, (2008),arXiv:0712.1102.

[t07/160] F. Yamada, T. Ono, H. Tanaka,G. Misguich, M. Oshikawa, and T. Sakak-ibara. Magnetic-Field Induced Bose-Einstein Condensation of Magnons andCritical Behavior in Interacting SpinDimer System TlCuCl3. J. Phys. Soc.Jpn., 77, 013701, (2008), arXiv:0711.2110.

[t07/161] G. Misguich. Quantum Spin Liquidsand fractionalization, 407433. Springer,(2007).

[t07/169] S.N. Majumdar, K. Mallick, andS. Nechaev. Bethe Ansatz in the BernoulliMatching Model of Random SequenceAlignment. Phys. Rev. E, 77, 011110,(2008), arXiv:0710.1030.

[t07/181] S. Prolhac and K. Mallick. CurrentFluctuations in the exclusion process andBethe Ansatz. J. Phys. A, 41, 175002,(2008), arXiv:0801.4659.

[t07/182] T. Antal, L. Krapivsky P., andK. Mallick. Molecular Spiders in One Di-mension. J. Stat. Mech., P08027, (2007),arXiv:0705.2594.

[t07/183] D. Lacoste, A. Lau, and K. Mallick.Fluctuation theorem and large deviationfunction for a solvable model of a molec-ular motor. Phys. Rev. E, 78, 011915,(2008), arXiv:0801.4152.

[t07/202] A.O. Gogolin, R.M. Konik, A.W.W.Ludwig, and H. Saleur. Counting statis-tics for the Anderson impurity model:Bethe ansatz and Fermi liquid study.Ann. Phys. (Leipzig), 16, 678701, (2007),arXiv:0804.3412.

[t07/226] C. Bena. Eect of a single impurityon the local density of states in monolayerand bilayer graphene. Phys. Rev. Lett.,100, 076601, (2008), arXiv:0706.4111.

[t07/227] K. Le Hur, S. Vishveshwara, andC. Bena. Double-gap proximity eect in

a carbon nanotube placed on a super-conducting substrate. Phys. Rev. B, 77,041406(R), (2008), arXiv:0706.4256.

[t08/003] Y. Avishai and J.M. Luck. Tight-binding electronic spectra on graphs withspherical topology. I. The eect of a mag-netic charge. J. Stat. Mech., P06007,(2008), arXiv:0801.1460.

[t08/004] C. Monthus and T. Garel. Non-equilibrium dynamics of polymers and in-terfaces in random media : conjecture ψ =ds/2 for the barrier exponent. J. Phys. A,41, 115002, (2008), arXiv:0712.3358.

[t08/024] Y. Avishai and J.M. Luck. Tight-binding electronic spectra on graphs withspherical topology. II. The eect of spin-orbit interaction. J. Stat. Mech., P06008,(2008), arXiv:0802.0795.

[t08/029] J.-P. Bouchaud and G. Biroli. Quan-tum plasticity and dislocation-induced su-persolidity. C.R. Physique, 9, 10671075,(2008), arXiv:0710.3087.

[t08/030] F. Lechenault, O. Dauchot, G. Biroli,and J.-P. Bouchaud. Lower bound on thefour-point dynamical susceptibility: Di-rect experimental test on a granular pack-ing. Europhys. Lett., 83, 46002, (2008),arXiv:0712.2036v1.

[t08/035] A. Poteryaev, M. Ferrero, A. Georges,and O. Parcollet. Eect of Crystal-Field Splitting and Inter-Band Hybridiza-tion on the Metal-Insulator Transitions ofStrongly Correlated Systems. Phys. Rev.B, 78, 045115, (2008), arXiv:0801.4356.

[t08/048] C. Monthus and T. Garel. Non equi-librium dynamics of disordered systems :understanding the broad continuum of rel-evant time scales via a strong-disorder RGin conguration space. J. Phys. A, 41,255002, (2008), arXiv:0802.2502.

[t08/049] R. Einert T., P. Näger, H. Orland,and R.R. Netz. Impact of loop statis-tics on the thermodynamics of RNA fold-ing. Phys. Rev. Lett., 101, 048103, (2008),arXiv:0802.3272.

[t08/079] G. Misguich, V. Pasquier, andF. Alet. Correlations and order param-eter at a Coulomb-crystal phase transi-tion in a three-dimensional dimer model.Phys. Rev. B, 78, 100402(R), (2008),arXiv:0803.2196.





















[t08/086] E. Gull, P. Werner, O. Parcollet, andM. Troyer. Continuous-time auxiliary eldMonte Carlo for quantum impurity mod-els. Europhys. Lett., 82, 57003, (2008),arXiv:0802.3222.

[t08/092] C. Monthus and T. Garel. Non-equilibrium dynamics of disordered sys-tems: renormalization ow towards an'innite disorder' xed point at largetimes. J. Stat. Mech., P07002, (2008),arXiv:0804.1847.

[t08/108] I. Aeck, L. Borda, and H. Saleur.Friedel oscillations and the Kondo screen-ing cloud. Phys. Rev. B, 77, 180404(R),(2008), arXiv:0802.0280.

[t08/113] A. Mehta, G.C. Barker, and J.M.Luck. Heterogeneities in granular dynam-ics. Proc. Nat. Acad. Sci., 105, 82448249,(2008).

[t08/122] C. Monthus and T. Garel. Equilib-rium of disordered systems : construct-ing the appropriate valleys in each samplevia strong disorder renormalization in con-guration space. J. Phys. A, 41, 375005,(2008), arXiv:0806.3335.

[t08/134] M.R. Evans, P. Ferrari, andK. Mallick. Matrix representation ofthe stationary measure for the multi-species TASEP. J. Stat. Phys., 135,217239, (2009), arXiv:0807.0327.

[t08/142] C. Godrèche and J.M. Luck. A record-driven growth process. J. Stat. Mech.,P11006, (2008), arXiv:0809.3377.

[t08/148] C. Monthus and T. Garel. Driveninterfaces in random media at nitetemperature: Existence of an anoma-lous zero-velocity phase at small externalforce. Phys. Rev. E, 78, 041133, (2008),arXiv:0803.4125.

[t08/150] M. Tarzia and G. Biroli. The ValenceBond Glass phase. Europhys. Lett., 82,67008, (2008), arXiv:0802.2653.

[t08/151] G. Biroli, J.-P. Bouchaud, A. Cav-agna, T.S. Grigera, and P. Verroc-chio. Thermodynamic signature of grow-ing amorphous order in glass-forming liq-uids. Nature Phys., 4, 771775, (2008),arXiv:0805.4427.

[t08/153] I. Sa, C. Bena, and A. Crépieux. acconductance and nonsymmetrized noise atnite frequency in quantum wires and car-bon nanotubes. Phys. Rev. B, 78, 205422,(2008), arXiv:0805.3932.

[t08/165] Z. Burda, J. Duda, J.M. Luck, andB. Waclaw. Localization of the maximalentropy random walk. Phys. Rev. Lett.,102, 160602, (2009), arXiv:0810.4113.

[t08/178] K.-S. Kim, A. Benlagra, and C. Pépin.Grüneisen ratio at the Kondo breakdownquantum critical point. Phys. Rev. Lett.,101, 246403, (2008), arXiv:0808.3908.

[t08/179] A. Benlagra and C. Pépin. Model ofQuantum Criticality in He3 bilayers Ad-sorbed on graphite. Phys. Rev. Lett., 100,176401, (2008), arXiv:0709.0354.

[t08/180] A. Benlagra and C. Pépin. He3bi-layers as a simple example of de-connement. Phys. Rev. B, 79, 045112,(2009), arXiv:0810.2280.

[t08/186] C. Monthus and T. Garel. Andersontransition on the Cayley tree as a travelingwave critical point for various probabil-ity distributions. J. Phys. A, 42, 075002,(2009), arXiv:0811.1422.

[t08/187] S. Furukawa, V. Pasquier, and J. Shi-raishi. Mutual Information and Boson Ra-dius in a c=1 Critical System in One Di-mension. Phys. Rev. Lett., 102, 170602,(2009), arXiv:0809.5113.

[t08/190] T.L. Dao, M. Ferrero, A. Georges,M. Capone, and O. Parcollet. Polar-ized superuidity in the attractive Hub-bard model with population imbalance.Phys. Rev. Lett., 101, 236405, (2008),arXiv:0807.2923.

[t08/191] L De Leo, C. Kollath, A. Georges,M. Ferrero, and O. Parcollet. Trappingand cooling fermionic atoms into the Mottand Néel states. Phys. Rev. Lett., 101,210403, (2008), arXiv:0807.0790.

[t08/192] M. Ferrero, P Cornaglia, L De Leo,O. Parcollet, G. Kotliar, and A. Georges.Valence-Bond Dynamical Mean-FieldTheory of Doped Mott Insulatorswith Nodal/Antinodal Dierentiation.Europhys. Lett., 85, 57009, (2009),arXiv:0806.4383.






















[t08/198] S. Prolhac. Fluctuations and skewnessof the current in the partially asymmetricexclusion process. J. Phys. A, 41, 365003,(2008), arXiv:0805.4118.

[t08/202] Y. Avishai and J.M. Luck. Magneti-zation of two coupled rings. J. Phys. A,42, 175301, (2009), arXiv:0812.2347.

[t08/206] L. Messio, J.C. Domenge, C. Lhuil-lier, L. Pierre, P. Viot, and G. Misguich.Thermal destruction of chiral order in atwo-dimensional model of coupled trihe-dra. Phys. Rev. B, 78, 054435, (2008),arXiv:0806.2259.

[t08/207] P. Ranjith, D. Lacoste, K. Mallick,and J.F. Joanny. Non-equilibriumself-assembly of a lament coupled toATP/GTP hydrolysis. Biophys. J., 96,21462159, (2009), arXiv:0809.2228.

[t08/209] S.N. Majumdar, K. Mallick, andS. Sabhapandit. Statistical Properties ofthe Final State in One-dimensional Ballis-tic Aggregation. Phys. Rev. E, 79, 021109,(2009), arXiv:0811.0908.

[t08/210] D. Lacoste and K. Mallick. Fluc-tuation Theorem for the ashing ratchetmodel of molecular motors. Phys. Rev. E,80, 021923, (2009), arXiv:0907.1570.

[t08/213] S. Prolhac, M.R. Evans, andK. Mallick. Matrix product solutionof the multispecies partially asymmetricexclusion process. J. Phys. A, 42, 165004,(2009), arXiv:0812.3293.

[t08/236] S. Prolhac and K. Mallick. Cumulantsof the current in the weakly asymmetricexclusion process. J. Phys. A, 42, 175001,(2009), arXiv:0902.0570.

[t08/244] E. Boulat, H. Saleur, and P. Schmit-teckert. Twofold advance in the theoreti-cal understanding of far-from-equilibriumproperties of interacting nanostructures.Phys. Rev. Lett., 101, 140601, (2008),arXiv:0806.3731.

[t08/246] Venuti L. Campos, H. Saleur, andP. Zanardi. Universal sub-leading termsin ground state delity. Phys. Rev. B, 79,092405, (2009), arXiv:0807.0104.

[t08/250] G. Misguich. Quantum spin liquids.(2008), arXiv:0809.2257.

[t08/265] P. Calabrese and A. Lefèvre. Entan-glement spectrum in one-dimensional sys-tems. Phys. Rev. A, 78, 032329, (2008),arXiv:0806.3059.

[t08/267] C. Pépin. Selective Mott transitionand heavy fermions. Phys. Rev. B, 77,245129, (2008), arXiv:0802.1498.

[t08/268] I. Paul, C. Pépin, and M.R. Nor-man. Multi-scale uctuations neara Kondo Breakdown Quantum CriticalPoint. Phys. Rev. B, 78, 035109, (2008),arXiv:0804.1808.

[t08/269] K.-S. Kim and C. Pépin. Vio-lation of Wiedemann-Franz law at theKondo breakdown quantum critical point.Phys. Rev. Lett., 102, 156404, (2009),arXiv:0811.0638.

[t08/282] M. Sega, P. Faccioli, F. Pederiva, andH. Orland. Kramers Theory for Confor-mational Transitions of Macromolecules.(2010), arXiv:0809.0027.

[t08/283] E. Autieri, P. Faccioli, M. Sega,F. Pederiva, and H. Orland. Dominant Re-action Pathways in High Dimensional Sys-tems. J. Chem. Phys., 130, 064106, (2009),arXiv:0806.0236.

[t08/284] J.-L. Sikorav, H. Orland, andA. Braslau. Mechanism of thermal re-naturation and hybridization of nucleicacids: Kramers process and universal-ity in Watson-Crick base pairing. J.Phys. Chem. B, 113, 37153725, (2009),arXiv:0808.1233.

[t08/285] H. Orland. Accelerated Sampling ofBoltzmann distributions. J. Phys. Soc.Jpn., 78, 103002, (2009), arXiv:0812.2587.

[t08/286] C. Azuara, H. Orland, M. Bon,P. Koehl, and M. Delarue. Incorporat-ing Dipolar Solvents with Variable Den-sity in Poisson-Boltzmann Electrostatics.Biophys. J., 95, 55875605, (2008).

[t08/287] P. Faccioli, M. Sega, F. Pederiva, andH. Orland. Stochastic dynamics and dom-inant protein folding pathways. Philos.Mag., 88, 40934099, (2008).

[t08/298] L. Simon, C. Bena, F. Vonau,D. Aubel, H. Nasrallah, M. Habar, andC. Peruchetti J. Symmetry of standingwaves generated by a point defect in epi-taxial graphene. Eur. Phys. J. B, 69, 351,(2009), arXiv:0807.2813.
























[t08/300] C. Bena. Greens functions and impu-rity scattering in graphene. Phys. Rev. B,79, 125427, (2009), arXiv:0807.1981.

[t08/304] C. Douarche, J.-L. Sikorav, andA. Goldar. Aggregation and Adsorption atthe Air-Water Interface of BacteriophageφX174 Single-Stranded DNA. Biophys. J.,94, 134146, (2008).

[t08/305] C. Douarche, R. Cortès, S.J. Roser,J.-L. Sikorav, and A. Braslau. DNA Ad-sorption at Liquid/Solid Interfaces. J.Phys. Chem. B, 112, 1367613679, (2008),arXiv:0809.4639.

[t09/026] A. Benlagra, K.-S. Kim, and C. Pépin.The Luttinger-Ward functional approachin the Eliashberg framework : A sys-tematic derivation of scaling for ther-modynamics near a quantum criticalpoint. J. Phys. C, 23, 145601, (2011),arXiv:0902.3630.

[t09/028] C. Monthus and T. Garel. Randomwetting transition on the Cayley tree : adisordered rst-order transition with twocorrelation length exponents. J. Phys. A,42, 165003, (2009), arXiv:0901.2797.

[t09/051] C. Monthus and T. Garel. Statisticsof the two-point transmission at Andersonlocalization transitions. Phys. Rev. B, 79,205120, (2009), arXiv:0903.1988.

[t09/064] A. Mehta, G.C. Barker, and J.M.Luck. Heterogeneities in granular mate-rials. Phys. Today, 62, 4045, (2009).

[t09/070] A. Ayyer, Carlen E. A., LebowitzJ. L., Mohanty P. K., D. Mukamel, andE.R. Speer. Phase diagram of the ABCmodel on an interval. J. Stat. Phys., 137,11661204, (2009), arXiv:0905.4849.

[t09/074] F. David and K.J. Wiese. FieldTheory of the RNA Freezing Transi-tion. J. Stat. Mech., P10019, (2009),arXiv:0906.1472.

[t09/087] C. Monthus and T. Garel. Ander-son transitions : multifractal or non-multifractal statistics of the transmissionas a function of the scattering geome-try. J. Stat. Mech., P07033, (2009),arXiv:0904.4547.

[t09/088] C. Monthus and T. Garel. Statis-tics of renormalized on-site energies and

renormalized hoppings for Anderson lo-calization models in dimensions d=2 andd=3. Phys. Rev. B, 80, 024203, (2009),arXiv:0905.4127.

[t09/089] J.M. Stéphan, S. Furukawa, G. Mis-guich, and V. Pasquier. Shannonand entanglement entropies of one- andtwo-dimensional critical wave functions.Phys. Rev. B, 80, 184421, (2009),arXiv:0906.1153.

[t09/094] T. Sarlat, A. Billoire, G. Biroli, andJ.-P. Bouchaud. Predictive power of MCT:Numerics and Finite size scaling for amean eld spin glass. J. Stat. Mech.,P08014, (2009), arXiv:0905.3333.

[t09/100] C. Godrèche, H. Grandclaude, andJ.M. Luck. Finite-time uctuations inthe degree statistics of growing networks.J. Stat. Phys., 137, 11171146, (2009),arXiv:0907.1470.

[t09/105] P. Werner, E. Gull, O. Parcollet, andA.J. Millis. Momentum-selective metal-insulator transition in the two-dimensionalHubbard model: An 8-site dynamical clus-ter approximation study. Phys. Rev. B, 80,045120, (2009), arXiv:0903.3012.

[t09/114] M. Ferrero, P Cornaglia, L De Leo,O. Parcollet, G. Kotliar, and A. Georges.Pseudogap opening and formation ofFermi arcs as an orbital-selective Motttransition in momentum space. Phys. Rev.B, 80, 064501, (2009), arXiv:0903.2480.

[t09/115] M. Aichhorn, L. Pourovskii, V. Vil-dosola, M. Ferrero, O. Parcollet,T. Miyake, A. Georges, and S. Bier-mann. Dynamical Mean-Field Theorywithin an Augmented Plane-Wave Frame-work: Assessing Electronic Correlationsin the Iron Pnictide LaFeAsO. Phys. Rev.B, 80, 085101, (2009), arXiv:0906.3735.

[t09/129] E. Gull, O. Parcollet, P. Werner, andA.J. Millis. On the momentum-sector-selective transition in the 8 site dynamicalmean eld approximation to the two di-mensional Hubbard model. Phys. Rev. B,80, 245102, (2009), arXiv:0909.1795.

[t09/155] C. Monthus and T. Garel. Statisti-cal properties of two-particle transmissionat Anderson transition. J. Phys. A, 42,475007, (2009), arXiv:0909.1894v1.





















[t09/157] A. Ayyer and K. Mallick. Exact re-sults for an asymmetric annihilation pro-cess with open boundaries. J. Phys. A, 43,045003, (2010), arXiv:0910.0693.

[t09/177] C. Monthus, B. Berche, and C. Chate-lain. Symmetry relation for multifractalspectra at random critical points. J. Stat.Mech., P12002, (2009), arXiv:0909.0584.

[t09/184] C. Godrèche, H. Grandclaude, andJ.M. Luck. Statistics of leaders and leadchanges in growing networks. J. Stat.Mech., P02001, (2010), arXiv:0911.3057.

[t09/208] C. Monthus and T. Garel. Eigenvaluemethod to compute the largest relaxationtime of disordered systems. J. Stat. Mech.,P12017, (2009), arXiv:0910.4833.

[t09/223] R. Candelier, O. Dauchot, andG. Biroli. Dynamical facilitation decreaseswhen approaching the granular glass tran-sition. Europhys. Lett., 92, 24003, (2010),arXiv:0912.0472v1.

[t09/224] R. Candelier, A. Widmer-Cooper,J.K. Kummerfeld, O. Dauchot, G. Biroli,P. Harrowell, and D.R. Reichman. Spa-tiotemporal Hierarchy of RelaxationEvents, Dynamical Heterogeneities, andStructural Reorganization in a Super-cooled Liquid. Phys. Rev. Lett., 105,135702, (2010), arXiv:0912.0193v1.

[t09/225] Darst Richard K., D.R. Reichman,and G. Biroli. Dynamical Heterogeneityin Lattice Glass Models. J. Chem. Phys.,132, 044510, (2010), arXiv:0911.0479.

[t09/226] G. Biroli, C. Kollath, and A. Läuchli.Eect of Rare Fluctuations on the Ther-malization of Isolated Quantum Systems.Phys. Rev. Lett., 105, 250401, (2010),arXiv:0907.3731v2.

[t09/227] F. Sausset, C. Toninelli, G. Biroli, andG. Tarjus. Bootstrap Percolation and Ki-netically Constrained Models on Hyper-bolic Lattices. J. Stat. Phys., 138, 411430, (2010), arXiv:0907.0938v2.

[t09/228] A. Andreanov, G. Biroli, and J.-P.Bouchaud. Mode-Coupling as a LandauTheory of the Glass Transition. Europhys.Lett., 88, 16001, (2009), arXiv:0903.4619.

[t09/229] M. Tarzia, G. Biroli, J.-P. Bouchaud,and A. Lefèvre. Anomalous non-linear

response of glassy liquids: general argu-ments and a Mode-Coupling approach.J. Chem. Phys., 132, 05450110 pages,(2010), arXiv:0812.3514.

[t09/230] R. Candelier, O. Dauchot, andG. Biroli. The building blocks of dynam-ical heterogeneities in dense granular me-dia. Phys. Rev. Lett., 102, 088001, (2009),arXiv:0811.0201.

[t09/231] C. Aron, G. Biroli, and L.F. Cuglian-dolo. Driven quantum coarsening.Phys. Rev. Lett., 102, 050404, (2009),arXiv:0809.0590.

[t09/232] G. Biroli, C. Chamon, and F. Zam-poni. Theory of the superglass phase.Phys. Rev. B, 78, 224306, (2009),arXiv:0807.2458.

[t09/239] G. Biroli and J.-P. Bouchaud. TheRandom First-Order Transition Theory ofGlasses: a critical assessment. (2009),arXiv:0912.2542v1.

[t09/246] D. Lacoste and K. Mallick. Fluc-tuation relations for molecular motors.(2009), arXiv:0912.0391.

[t09/247] P. Ranjith, K. Mallick, J.F. Joanny,and D. Lacoste. Role of ATP-hydrolysis inthe treadmilling of a single Role of ATP-hydrolysis in the treadmilling of a singleactin lament. Biophys. J., 98, 14181427,(2010), arXiv:0908.0657.

[t09/249] K. Mallick. Developpements Re-cents en Physique Statistique Loin del'Equilibre. (2009).

[t09/251] M. Barthélémy, J.P. Nadal, andH. Berestycki. Disentangling collectivetrends from local dynamics. Proc. Nat.Acad. Sci., 107, (2010), arXiv:0909.1490.

[t09/252] M. Woelki and K. Mallick. Transfermatrices for the totally asymmetric simpleexclusion process. J. Phys. A, 43, 185003,(2010), arXiv:1001.1064.

[t09/255] R Chetrite and K. Mallick. Fluc-tuation Relations for Quantum Marko-vian Dynamical Systems. (2010),arXiv:1002.0950.

[t09/267] A. Lefèvre. Aging is - almost - likeequilibrium. (2009), arXiv:0910.0397.
























[t09/272] A. Crisanti, C. De Dominicis, andT. Sarlat. Low temperature spin glassuctuations: expanding around a spheri-cal approximation. Eur. Phys. J. B, 74,139149, (2010), arXiv:0909.2556.

[t09/275] K.-S. Kim and C. Pépin. Quan-tum Boltzman equation study for theKondo breakdown quantum critical point.J. Phys.: Condens. Matter, 22, 025601,(2010), arXiv:0904.1041.

[t09/276] B. Efetov K., C. Pépin, and H. Meier.Exact bosonization for an interactingFermi gas in arbitrary dimensions.Phys. Rev. Lett., 103, 186403, (2009),arXiv:0907.3243.

[t09/279] A. Crisanti and C. De Dominicis.Sherrington-Kirkpatrick model near T =Tc: expanding around the Replica Sym-metric Solution. J. Phys. A, 43, 055002,(2010), arXiv:0910.4091.

[t09/305] P. Faccioli, A. Lonardi, and H. Or-land. Dominant reaction pathways inprotein folding: A direct validationagainst molecular dynamics simulations.J. Chem. Phys., 133, 045104, (2010),arXiv:0912.0037.

[t09/306] O. Corradini, P. Faccioli, and H. Or-land. Simulating Stochastic Dynamics Us-ing Large Time Steps. Phys. Rev. E, 80,061112, (2009), arXiv:0907.2948.

[t09/309] C. Godrèche and A.J. Bray. Nonequi-librium stationary states and phase tran-sitions in directed Ising. J. Stat. Mech.,2009, P12016, (2009).

[t09/310] C. Godrèche, S.N. Majumdar, andG. Schehr. The longest excursion of sto-chastic processes in nonequilibrium sys-tems. Phys. Rev. Lett., 102, 240602,(2009).

[t09/311] P. Koehl, H. Orland, and M. De-larue. Beyond the Poisson-BoltzmannModel: Modeling Biomolecule-Water andWater-Water Interactions. Phys. Rev.Lett., 102, 087801, (2009).

[t09/312] P. Koehl, H. Orland, and M. Delarue.Computing Ion Solvation Free EnergiesUsing the Dipolar Poisson Model. J. Phys.Chem. B, 113, 56945697, (2009).

[t09/313] C. Micheletti and H. Orland. MIS-TRAL: a tool for energy-based multiplestructural alignment of proteins. Bioin-formatics, 25, 26632669, (2009).

[t09/322] K. Mallick. Some recent developmentsin non-equilibrium statistical physics. vol-ume 73 of Pramana J. Phys., 417451,(2009).

[t09/330] C. Bena. The local density ofstates in the presence of impurity scat-tering in graphene at high magneticeld. Phys. Rev. B, 83, 045409, (2010),arXiv:0906.2282.

[t09/331] C. Bena. The tunneling conduc-tance between a superconducting STMtip and an out-of-equilibrium carbon nan-otube. Phys. Rev. B, 82, 035312, (2010),arXiv:0909.0867.

[t09/333] P. Koehl, H. Orland, and M. De-larue. Solvation of Ion Pairs: The Poisson-Langevin Model. International Confer-ence on Signal Processing Systems (ICSPS2009), Singapore, SINGAPORE, (2009).

[t10/002] C. Monthus and T. Garel. Randomwalk in two-dimensional self-ane randompotentials : strong disorder renormaliza-tion approach. Phys. Rev. E, 81, 011138,(2010), arXiv:0910.0111.

[t10/004] C. Monthus and T. Garel. Statistics ofrst-passage times in disordered systemsusing backward master equations andtheir exact renormalization rules. J. Phys.A, 43, 095001, (2010), arXiv:0911.5649.

[t10/009] C. Monthus and T. Garel. Matchingbetween typical uctuations and large de-viations in disordered systems : applica-tion to the statistics of the ground stateenergy in the SK spin-glass model. J. Stat.Mech., P02023, (2010), arXiv:0912.2875.

[t10/015] B. Efetov K., C. Pépin, and H. Meier.Describing systems of interacting fermionsby boson models: exact mapping inarbitrary dimension and applications.Phys. Rev. B, 82, 235120, (2010),arXiv:1001.1552.

[t10/018] B. Efetov K., C. Pépin, and H. Meier.Reply to the Comment by Galanakis etal on the paper "Exact bosonization foran interacting Fermi gas in arbitrary di-mensions". Phys. Rev. Lett., 105, 159702,(2010), arXiv:1001.1626.






















[t10/019] K.-S. Kim and C. Pépin. The ther-mopower as a signature of quantum criti-cality in heavy fermions. Phys. Rev. B, 81,205108, (2010), arXiv:1002.2612.

[t10/043] C. Monthus and T. Garel. Many-body localization transition in a latticemodel of interacting fermions: statisticsof renormalized hoppings in congurationspace. Phys. Rev. B, 81, 134202, (2010),arXiv:1001.2984.

[t10/049] M. Barthélémy, C. Godrèche, andJ.M. Luck. Fluctuation eects inmetapopulation models: percolation andpandemic threshold. J. Theor. Biol., 267,554564, (2010), arXiv:1004.1553.

[t10/051] Z. Burda, J. Duda, J.M. Luck, andB. Waclaw. The various facets of randomwalk entropy. Acta Phys. Pol. B, 41, 949987, (2010), arXiv:1004.3667.

[t10/063] L. Krapivsky P. and K. Mallick. Poly-mer translocation through a pore. J. Stat.Mech. (to appear), (2010).

[t10/064] K. Mallick. COURS ALEA 2010: Pro-cessus d'Exclusion Asymetrique. ALEA,CIRM (Luminy), (2010).

[t10/069] C. Monthus and T. Garel. Ran-dom cascade models of multifractality :real-space renormalization and travelling-waves. J. Stat. Mech., P06014, (2010),arXiv:1004.1537.

[t10/078] C. Godrèche and J.M. Luck. On lead-ers and condensates in a growing net-work. J. Stat. Mech., P07031, (2010),arXiv:1006.0587.

[t10/080] C. Monthus and T. Garel. Ander-son localization of phonons in dimen-sion d=1,2,3 : nite-size properties ofthe Inverse Participation Ratios of eigen-states. Phys. Rev. B, 81, 224208, (2010),arXiv:1003.5988.

[t10/082] J.M. Luck and A. Mehta. The eectsof grain shape and frustration in a granu-lar column near jamming. Eur. Phys. J.B, 77, 505521, (2010), arXiv:1006.3397.

[t10/100] A. Ayyer and V. Strehl. Thespectrum of an asymmetric annihilationprocess. DMTCS Proceedings, (2010),arXiv:1008.2134.

[t10/102] C. Monthus and T. Garel. Randomwalk in a two-dimensional self-ane ran-dom potential : properties of the anoma-lous diusion phase at small externalforce. Phys. Rev. E, 82, 021125, (2010),arXiv:1003.1627.

[t10/106] S. Prolhac. Tree structures for thecurrent uctuations in the exclusion pro-cess. J. Phys. A, 43, 105002, (2010),arXiv:0911.3618.

[t10/109] G. Biroli, L.F. Gugliandolo, and A. Si-cilia. Kibble-Zurek mechanism and in-nitely slow annealing through criticalpoints. Phys. Rev. E, 81, 050101, (2010),arXiv:1001.0693.

[t10/110] F. Sausset, G. Biroli, and J. Kurchan.Do solids ow? J. Stat. Phys., 140, 718721, (2010), arXiv:1001.0918.

[t10/113] C. Roth, S.M. Kang, M. Batty,and M. Barthélémy. Structure of ur-ban movements: polycentric activity andentangled hierarchical ows. (2011),arXiv:1001.4915.

[t10/115] C. Kollath, G. Roux, G. Biroli, andA. Läuchli. Statistical properties ofthe spectrum the extended Bose-Hubbardmodel. J. Stat. Mech., P08011, (2010),arXiv:1004.2203.

[t10/116] A. Branschadel, E. Boulat, H. Sa-leur, and P. Schmitteckert. Shot noise inthe self-dual Interacting Resonant LevelModel. (2010), arXiv:1004.4811.

[t10/117] J.M. Stéphan, G. Misguich, andV. Pasquier. Rényi entropy of a line intwo-dimensional Ising models. Phys. Rev.B (to appear), (2010), arXiv:1006.1605.

[t10/121] C. Cammarota, G. Biroli, M. Tarzia,and G. Tarjus. Renormalization GroupAnalysis of the Random First-Order Tran-sition. Phys. Rev. Lett., 106, 115705,(2011), arXiv:1007.2509v1.

[t10/122] E. Gull, M. Ferrero, O. Parcollet,A. Georges, and A.J. Millis. Momen-tum space anisotropy and pseudogaps:a comparative cluster dynamical meaneld analysis of the doping-driven metal-insulator transition in the two dimensionalHubbard model. Phys. Rev. B, 82, 155101,(2010), arXiv:1007.2592.























[t10/123] B. Sciolla and G. Biroli. QuantumQuenches and O-Equilibrium Dynami-cal Transition in the Innite-DimensionalBose-Hubbard Model. Phys. Rev. Lett.,105, 220401, (2010), arXiv:1007.5238v2.

[t10/124] S. a Beccara, P. Faccioli, G. Gar-beroglio, M. Sega, F. Pederiva, and H. Or-land. Dominant folding pathways of apeptide chain, from ab-initio quantum-mechanical simulations. J. Chem. Phys.,134, (2011), arXiv:1007.5235.

[t10/127] J.D. Pillet, C. Quay, P. Morn,C. Bena, A. Levy Yeyati, and P. Joyez. Re-vealing the electronic structure of a carbonnanotube carrying a supercurrent. NaturePhys., 6, 965, (2010), arXiv:1005.0443.

[t10/133] A. Ayyer, J.L. Lebowitz, and E.R.Speer. On Some Classes of Open Two-Species Exclusion Processes. (2010),arXiv:1008.4721.

[t10/136] C. Monthus and T. Garel. Andersonlocalization transition with long-rangedhoppings : analysis of the strong multi-fractality regime in terms of weighted Levysums. J. Stat. Mech., P09015, (2010),arXiv:1006.1510.

[t10/157] A. Billoire. Distribution of timescales in the Sherrington-Kirkpatrickmodel. J. Stat. Mech., P11034, (2010),arXiv:1003.6086v3.

[t10/158] A. Billoire, I. Kondor, J Lukic, andE. Marinari. Large random correlationsin individual mean eld spin glass sam-ple. J. Stat. Mech., P02009, (2011),arXiv:1010.3237v2.

[t10/179] A. Billoire. What makes slow sam-ples slow in the Sherrington-Kirkpatrickmodel. J. Phys. A, 44, 075001, (2011),arXiv:1011.3420.

[t10/192] J. Olejarz, L. Krapivsky P., andS. Redner. Zero-Temperature Freezing inThree-Dimensional Kinetic Ising Model.(2010), arXiv:1011.2903.

[t10/193] L. D'Alessio and L. Krapivsky P. ALight impurity in an Equilibrium Gas.(2010), arXiv:1009.3814.

[t10/194] L. Krapivsky P. and S. Redner.First Passage in Innite Paraboloidal Do-mains. J. Stat. Mech., P11028, (2010),arXiv:1009.2530.

[t10/217] K. Mallick, M. Moshe, and H. Orland.A eld-theoretic approach to nonequilib-rium work identities. J. Phys. A, 44,095002, (2011), arXiv:1009.4800.

[t10/218] K. Tsekouras, D. Lacoste, K. Mallick,and J.F. Joanny. Force generation by aparallel array of actin laments. (2011),arXiv:1101.1180.

[t10/225] J.M. Stéphan, G. Misguich, andF. Alet. Geometric entanglement andAeck-Ludwig boundary entropies in crit-ical XXZ and Ising chains. Phys. Rev. B,82, 180406(R), (2011), arXiv:1007.4161.

[t10/249] F. Vonau, P.B. Pillai, D. Aubel,M.M. De Souza, C. Bena, and L. Simon.Superlattice of resonators on monolayergraphene created by intercalated gold nan-oclusters. Europhys. Lett., 91, 66004,(2011), arXiv:1006.5850.

[t10/251] C. Bena and L. Simon. Dirac pointmetamorphosis from third-neighbor cou-plings in graphene and related materi-als. Phys. Rev. B, 83, 115404, (2011),arXiv:1007.3907.

[t10/259] M. Ferrero, O. Parcollet, A. Georges,G. Kotliar, and Basov D. Interplanecharge dynamics in a valence-bond dy-namical mean-eld theory of cuprate su-perconductors. Phys. Rev. B, 82, 054502,(2010), arXiv:1001.5051.

[t10/260] Z. Bertalan, H. Nishimori, and H. Or-land. Accelerated stochastic sampling ofdiscrete statistical systems. Phys. Rev. E,82, 056704, (2010).

[t10/261] M. Bon and H. Orland. Predictionof RNA secondary structures with pseudo-knots. Physica A, 389, 29872992, (2010).

[t10/262] X. Man, D. Andelman, and H. Or-land. Block Copolymer at Nano-PatternedSurfaces. Macromolecules, 43, 72617268,(2010).

[t10/263] R. Potestio, C. Micheletti, and H. Or-land. Knotted vs. Unknotted Proteins:Evidence of Knot-Promoting Loops. PLoSComput Biol, 6, e1000864, (2010).

[t10/264] G. Mazzola, S. a Beccara, P. Fac-cioli, and H. Orland. Fluctuationsin the Ensemble of Reaction Pathways.J. Chem. Phys. (to appear), (2011),arXiv:1012.3424.
























[t10/265] J. Dubail and J.M. Stéphan. Universalbehavior of a bipartite delity at quantumcriticality. (2011), arXiv:1010.3716.

[t10/268] L. Berthier, G. Biroli, J.-P. Bou-chaud, and R.L. Jack. Overview of dier-ent characterisations of dynamic hetero-geneity. Oxford University Press, (2011),arXiv:1009.4765v2.

[t10/269] C. Aron, G. Biroli, and L.F. Cuglian-dolo. Symmetries of generating functionalsof Langevin processes with colored multi-plicative noise. J. Stat. Mech., P11018,(2010), arXiv:1007.5059v2.

[t10/270] C. Aron, G. Biroli, and L.F. Cuglian-dolo. Coarsening of disordered quantumrotors under a bias voltage. Phys. Rev. B,82, 174203, (2010), arXiv:1005.2414v2.

[t10/271] G. Biroli, G. Semerjian, andM. Tarzia. Anderson Model on BetheLattices: Density of States, LocalizationProperties and Isolated Eigenvalue. vol-ume 184 of Prog. Theor. Phys. (Suppl.), 187199, (2010), arXiv:1005.0342v2.17th Yukawa International Seminar 2009(YKIS2009) "Frontiers in NonequilibriumPhysics Fundamental Theory, Glassy &Granular Materials, and ComputationalPhysics ", Yukawa Institute for Theo-retical Physics (YITP), Kyoto University,Kyoto, Japan, 2009-07-21/2009-08-21.

[t10/272] G. Biroli, B. Clark, L. Foini, andF. Zamponi. Leggett's bound for amor-phous solids. Phys. Rev. B, 83, 094530,(2011), arXiv:1011.2863.

[t10/273] L. Berthier and G. Biroli. A theoreti-cal perspective on the glass transition andnonequilibrium phenomena in disorderedmaterials. Rev. Mod. Phys. (to appear),(2011), arXiv:1011.2578v1.

[t10/274] A. Crisanti and C. De Dominicis.Low-temperature mass spectrum in theIsing spin glass. Europhys. Lett., 92,17003, (2010), arXiv:1010.0637v1.

[t10/275] C. Brito, O. Dauchot, G. Biroli, andJ.-P. Bouchaud. Elementary excitationmodes in a granular glass above jam-ming. Soft Matter, 6, 30133022, (2010),arXiv:1003.1529v1.

[t10/280] C. Crauste-Thibierge, C. Brun,F. Ladieu, D. L'Hote, G. Biroli, and J.-P.

Bouchaud. Evidence of Growing SpatialCorrelations at the Glass Transitionfrom Nonlinear Response Experiments.Phys. Rev. Lett., 104, 165703, (2010),arXiv:1002.0498v2.

[t10/282] F. Lechenault, R. Candelier, O. Dau-chot, J.-P. Bouchaud, and G. Biroli.Super-diusion around the rigiditytransition: Lévy and the Lilliputians.Soft Matter, 6, 30593064, (2010),arXiv:1001.1765v1.

[t10/286] A. Rancon-Schweiger, A. Benlagra,and C. Pépin. Activation gap in thespecic heat measurements for 3He bilay-ers. Phys. Rev. B, 83, 073102, (2011),arXiv:1005.1905.

[t10/287] K.-S. Kim and C. Pépin. Ther-mopower as a ngerprint of the Kondobreakdown quantum critical point.Phys. Rev. B, 83, 073104, (2011),arXiv:1005.3354.

[t10/288] C. Pépin, M.R. Norman, S. Bur-din, and A. Ferraz. Modulated SpinLiquid: A New Paradigm for URu2Si2.Phys. Rev. Lett., 106, 106601, (2011),arXiv:1010.1237.

[t11/005] D. Gredat, I. Dornic, and J.M. Luck.On an imaginary exponential functional ofBrownian motion. J. Phys. A, 44, 175003,(2011), arXiv:1101.1173.

[t11/009] L. Krapivsky P. and J.M. Luck. Dy-namics of a quantum particle in low-dimensional disordered systems with ex-tended states. J. Stat. Mech., P02031,(2011), arXiv:1101.2101.

[t11/010] C. Monthus and T. Garel. Elastic ran-dom networks : strong disorder renormal-ization approach. J. Phys. A, 44, 085001,(2011), arXiv:1010.1627.

[t11/012] G. Verley, K. Mallick, and D. Lacoste.Modied Fluctuation-dissipation theoremfor non-equilibrium steady-states and ap-plications to molecular motors. (2010),arXiv:1009.4123.

[t11/018] C. Lhuillier and G. Misguich. Intro-duction to Quantum Spin Liquids, 2341.Springer, (2011).





















[t11/020] C. Monthus and T. Garel. Andersonlocalization on the Cayley tree : multifrac-tal statistics of the transmission at criti-cality and o criticality. J. Phys. A, 44,145001, (2011), arXiv:1101.0982.

[t11/027] M. Barthélémy. Spatial Networks.(2011), arXiv:1010.0302.

[t11/042] M. Colangeli, C. Maes, andB. Wynants. A meaningful expan-sion around detailed balance. J. Phys. A,44, 095001, (2011), arXiv:1101.3487.

[t11/043] M. Baiesi, C. Maes, and B. Wynants.The modied SutherlandEinstein rela-tion for diusive nonequilibria. Proc. R.Soc. A, (2011), arXiv:1101.3227.

[t11/046] Arita C., A. Ayyer, K. Mallick,and S. Prolhac. Recursive structuresin the multispecies TASEP. (2011),arXiv:1104.3752.

[t11/049] C. Monthus and T. Garel. A criticalDyson hierarchical model for the Ander-son localization transition. J. Stat. Mech.,P05005, (2011), arXiv:1102.4701.

[t11/050] C. Monthus. Non-equilibrium steadystates : maximization of the Shannon en-tropy associated to the distribution of dy-namical trajectories in the presence of con-straints. J. Stat. Mech., P03008, (2011),arXiv:1011.1342.

[t11/053] A. Branschaedel, E. Boulat, H. Sa-leur, and P. Schmitteckert. NumericalEvaluation of Shot Noise using Real TimeSimulations. (2010), arXiv:1004.4784.

[t11/067] M. Castellana and L. Zdeborova.Adversarial Satisability Problem.J. Stat. Mech., P03023, (2011),arXiv:1011.1273v1.

[t11/070] F. Krzakala, F. Ricci-Tersenghi,D. Sherrington, and L. Zdeborova.No spin glass phase in ferromagneticrandom-eld random-temperature scalarGinzburg-Landau model. J. Phys. A, 44,042003, (2011), arXiv:1008.4497v1.

[t11/071] F. Krzakala and L. Zdeborova. Glassyaspects of melting dynamics (On meltingdynamics and the glass transition, PartI). J. Chem. Phys., 134, 034512, (2011),arXiv:1006.2480.

[t11/072] F. Krzakala and L. Zdeborova. Glassydynamics as a melting process (On melt-ing dynamics and the glass transition, PartII). J. Chem. Phys., 134, 034513, (2011),arXiv:1006.2479.

[t11/073] Y. Matsuda, H. Nishimori, L. Zde-borova, and F. Krzakala. Random-eldp-spin glass model on regular randomgraphs. J. Phys. A (to appear), (2011),arXiv:1101.5863.

[t11/077] I. Brihuega, P. Mallet, S. Bose,C. Bena, C. Michaelis, L. Vitali,F. Varchon, L. Magaud, K. Kern,and J. Veuillen Y. Quasiparticle Chiralityin Epitaxial Graphene Probed at theNanometer Scale. Phys. Rev. Lett., 101,206802, (2008), arXiv:0806.2616.

[t11/079] C. Bena and G. Montambaux. Re-marks on the tight-binding model ofgraphene. New J. Phys., 11, 095003,(2009), arXiv:0712.0765.

[t11/084] B. Bauer, Carr L.D., H.G. Ev-ertz, A. Feiguin, J. Freire, S. Fuchs,L. Gamper, J. Gukelberger, E. Gull,S. Guertler, A. Hehn, R. Igarashi, S.V.Isakov, D. Koop, P.N. Ma, P. Mates,H. Matsuo, O. Parcollet, G. Pawlowski,J.D. Picon, L. Pollet, E. Santos, V.W.Scarola, U. Schollwoeck, C. Silva,B. Surer, S. Trebst, M. Troyer, M.L. Wall,P. Werner, and S. Wessel. The ALPSproject release 2.0: Open source softwarefor strongly correlated systems. J. Stat.Mech., P05001, (2011), arXiv:1101.2646.

[t11/088] G. Vernizzi and H. Orland. Randommatrix theory and RNA folding. OxfordUniversity Press, (2011).

[t11/089] M. Bon and H. Orland. TT2NE: Anovel algorithm to predict RNA secondarystructures with pseudoknots. Nucl. AcidsRes., doi: 10.1093/nar/gkr240, (2011),arXiv:1010.4490.

[t11/090] X. Man, D. Andelman, H. Orland,P. Thebault, P.H. Liu, P. Guenoun,J. Daillant, and S. Landis. Organizationof Block Copolymers using NanoImprintLithography: Comparison of Theory andExperiments. Macromolecules, 44, 22062211, (2011), arXiv:1007.4733.

[t11/091] H. Orland. Generating Transi-tion Paths by Langevin Bridges. J.






















Chem. Phys., 134, 174114, (2011),arXiv:1102.3442.

[t11/092] R. Einert T., H. Orland, and R.R.Netz. Secondary structure formationof homopolymeric single-stranded nucleicacids including force and loop entropy: im-plications for DNA hybridization. Eur.Phys. J. E (to appear), (2011).

[t11/096] A Lazarescu and K. Mallick. An Ex-act Formula for the Statistics of the Cur-rent in the TASEP with Open Boundaries.(2011).

[t11/098] C. Godrèche. Dynamics ofthe directed Ising chain. (2011),arXiv:1102.0141.

[t11/101] A. Crisanti and C. De Dominicis.Stability of the Parisi solution for theSherringtonKirkpatrick model near T= 0. J. Phys. A, 44, 15006, (2011),arXiv:1101.5233v1.

[t11/102] J.M. Stéphan, G. Misguich, andV. Pasquier. Phase transition in the

Rényi-Shannon entropy of Luttinger liq-uids. (2011), arXiv:1104.2544.

[t11/103] L. Messio, C. Lhuillier, and G. Mis-guich. Lattice symmetries and regularstates in classical frustrated antiferromag-nets. (2011), arXiv:1101.1212.

[t11/106] Berthier L., Biroli G., Bouchaud J.-P., Cipelletti L., and van Saarloos W.,editors. Dynamical Heterogeneities inGlasses, Colloids, and Granular Media.Oxford University Press, USA, (2011).

[t11/108] A. Ayyer. Algebraic Properties of aDisordered Asymmetric Glauber Model.J. Stat. Mech., 1102, P02034, (2011),arXiv:1012.0875.

[t11/136] M. Bauer and D. Bernard. Quan-tum Stochastic Processes: A Case Study.(2011), arXiv:1101.3472.

[t11/154] C. Maes, K. Netocny, andB. Wynants. Monotone return tosteady nonequilibrium. Phys. Rev. Lett.(to appear), (2011), arXiv:1102.3028.











CHAPTERD

Appendices

D.1 Awards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

D.2 Summary of publications . . . . . . . . . . . . . . . . . . . . . . . . . . 187

D.3 Fundings and grants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188

D.4 Habilitation thesis - Habilitation à diriger des recherches . . . . . . 197

D.5 Doctoral schools - Écoles doctorales . . . . . . . . . . . . . . . . . . . 198

D.6 PhD defenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

D.7 Current PhD students . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

D.8 Postdocs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

D.9 Internships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

D.10 IPhT lectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

D.11 Teaching in university or grandes écoles . . . . . . . . . . . . . . . 208

D.12 Teaching in summer schools . . . . . . . . . . . . . . . . . . . . . . . . 210

D.13 Weekly seminars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

D.14 Claude Itzykson meetings . . . . . . . . . . . . . . . . . . . . . . . . . 215

D.15 Organization of workshops and conferences . . . . . . . . . . . . . . . 218

D.16 Research administration . . . . . . . . . . . . . . . . . . . . . . . . . . 221

D.17 IPhT and high performance computing . . . . . . . . . . . . . . . . . 223

D.18 Scientic editing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

D.19 Internal organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

D.19.1 Aliation, direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

D.19.2 Committees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

D.19.3 Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

D.20 Permanent members of IPhT . . . . . . . . . . . . . . . . . . . . . . . 228

185


D.1 AwardsJean-Paul BLAIZOTJ. Hans D. Jensen prize awarded by Ruprecht-Karls University (Heidelberg). February 2009.

Claude GODRÈCHEChevalier des palmes académiques. September 2009.

Ivan KOSTOVServant prize awarded by the Academy of Sciences. September 2007.

Matt LUZUM2011 Dissertation in Nuclear Physics Award for his thesis, awarded by the American PhysicalSociety. November 2010.

Ruben MINASIANRecipient of a Friedrich Wilhelm Bessel Research Award after having been nominated for this awardby the German scientist Prof. Dr. Stefan Theisen, Max-Planck-Institut fuer Gravitationsphysik,Golm/Potsdam. November 2007.

Cécile MONTHUSGustave Ribaud prize awarded by the Academy of Sciences. September 2007.

Olivier PARCOLLETErnest Déchelle prize awarded by the Academy of Sciences. November 2009.

Hubert SALEURSilver medal of CNRS. May 2011.

Jean ZINN-JUSTINAcademy of Science. March 2011.

Appendices 187

D.2 Summary of publications

All the data given here consider only publications signed with IPhT among theinstitutions, and published in reviews indexed in the ISI-Web of Science database.

They have been etablished by the IST, the oce of the CEA in charge of thisdomain, in May 2011. Consequently, these data concern the full calendar years from2007 to 2010, and not 2011.

Note that the year corresponds to the date of the publication in the review, butnot the date of submission of the manuscript, or the publication as preprint onArXiv.org.

Year 2007 2008 2009 2010 TotalNb of publications 166 186 191 186 729

We give below the total number of publications on 20072010 for journals withat least 5 publications.

Journal of High Energy Physics 95Physical Review D 71Physical Review Letters 53Physical Review B 45Journal of Statistical Mechanics 42Nuclear Physics A 41Journal of Physics A-Mathematical and Theoretical 40Nuclear Physics B 40Journal of Cosmology and Astroparticle Physics 28Physical Review E 27Physics Letters B 21Physical Review C 17Acta Physica Polonica B 13EPL 13Journal of Statistical Physics 13Nuclear Physics B-Proceedings Supplements 10Journal of Physics G-Nuclear and Particle Physics 9European Physical Journal B 8Astronomy & Astrophysics 6Communications in Mathematical Physics 6Journal of Chemical Physics 6European Physical Journal C 6Classical and Quantum Gravity 5Progress of Theoretical Physics Supplement 5Other journals 109


D.3 Fundings and grants

European Research Council ERC (FP7)

Person Type Topic Dates

I. Bena ERC Starting GrantString-QCD-BH: String Theory, QCDand Black Holes

01/01/201031/12/2014

M. Graña ERC Starting GrantOberservableString: The Low EnergyLimit of String Theory and theObservable World

01/02/201131/01/2016

D. Kosower ERC Advanced GrantMM-PGT: Modern Methods forPerturbative Gauge Theories

01/01/200931/12/2013

G. Servant ERC Starting GrantCosmo@LHC: Cosmology at theCERN Large Hadron Collider

01/07/2008-30/06/2013

Individual Marie-Curie Fellowships (FP6, FP7)

Person Type Topic Dates

C. BenaIntra-EuropeanFellowship, FP6

TSINANO : Transport in StronglyInteracting Nanosystems

06/11/200605/11/2008

I. BenaInternational Reinte-gration Grant, FP6

String Theory, QCD and Black Holes01/09/200731/08/2009

M. FrigerioEuropean IndividualFellowships, FP7

BEYOND NEUTRINO MASS : Fromneutrino mass phenomenology to theparticle physics theory beyond theStandard Model and related signaturesin cosmology and colliders

01/09/200731/08/2009

J. LopezAlbacete

Intra-EuropeanFellowship, FP7

HICLHC : Heavy Ion Collisions at theLHC : Strong coupling techniques forhigh density QCD

01/06/200930/05/2011

C. MarquetOutgoingInternationalFellowship, FP6

Study of newly-discovered matter invery energetic collisions of hadrons orheavy ions

01/06/200731/05/2010

E. Sefusatti Intra-EuropeanFellowship, FP7

AGILE : Perturbative Approaches toGravitational Instability and Lensingin Cosmology

05/01/201004/01/2012

Appendices 189

Marie Curie Initial Training Networks (ITN), International Research Sta ExchangeScheme (IRSES) and Research Training Networks (RTN)

LocalContact

Topic Partners Dates

P. BraxC. CapriniM. CirelliC. SavoyF. Vernizzi

UniverseNet : Theorigin of our universe:Seeking links betweenfundamental physicsand cosmology

Coord. : Subir Sarkar (OxfordUniversity)Part. : Lancaster King's CollegeLondonIFAE BarcelonaBonnLMU MunchenNiels Bohr Institute CopenhagenCERNHelsinkiIoanninaINFN ItalyAPC ParisWarsawSeoul University

2008-2010

R. BrittoD. KosowerG. Soyez(Part)

LHCPhenoNet :Advanced ParticlePhenomenology in theLHC era

Coord. : German Rodrigo (Institutode Fisica Corpuscular , Valencia)

01/01/2011-31/12/2013

F. David(Part 13)

ENRAGE : EuropeanNetwork on RandomGEometry

Coord. : R. Loll, Utrecht UniversityPart 2 : Barcelona UnivPart 3 : Bielefeld UnivPart 4 : Herio-Watt UnivPart 5 : Iceland UnivPart 6 : ICL, UKPart 7 : Krakow UnivPart 8 : Leipzig UnivPart 9 : Copenhagen UnivPart 10 : NRD, AthensPart 11 : Univ Paris-SudPart 12 : Oxford Univ

01/09/2005-31/08/2009

B.Duplantier(Part.)

CASIMIR, NewTrends andApplications of theCasimir Eect

Coord. : A. Lambrecht, LKB01/01/2008-12/31/2012

I. Kostov(Part 3)

UNIFY : Unicationof Fundamental Forcesand Applications

Coord : M. S. Costa, Univ. de PortoPart 2 : Univ. de BerlinPart 4 : Perimeter Institute,Part 5 : C.N. Yang Institute forTheoretical Physics,Part 6 : Univ. de Tokyo

01/06/2011-31/05/2015


J.-M.Normand

PRACE : Partnershipfor AdvancedComputing in Europe

Austria: JKUBulgaria: NCSACyprus: CaSToRCCzech Republic: VSBFinland: CSCFrance: GENCIGermany: GCSGreece: GRNETIreland: ICHECItaly: CINECAThe Netherlands: NCFNorway: SIGMA - UNINETTPoland: PSNCPortugal: FCTUCSerbia: IPBSpain: BSCSweden: SNICSwitzerland: ETH ZurichTurkey: UYBHMUK: EPSRC

2008-2012

C. Savoy(Part 2)

QUEST : The QuestFor Unication:Theory ConfrontsExperimentsfollowed byUNILHC : Unicationin the LHC era

Coord. : I. Antoniadis (EcolePolytechnique, Palaiseau)Part 3 : Bonn UniversityPart 4 : AUTH, GreecePart 5 : INFN, ItalyPart 6 : ICTP, ItalyPart 7 : IST, PortugalPart 8 : UAM, SpainPart 9 : UVEG, SpainPart 10 : UOXF.DR, UKPart 11 : Warsaw Univ.Part 12 : CERN,Geneva

01/10/2004-30/09/200801/10/2009-30/09/2013

Appendices 191

P. Vanhove(Part.)

ForcesUniverse :Constituents,Fundamental Forcesand Symmetries of theUniverse

Coord. : Dieter Luest ,Ludwig-Maximilians-UniversitätMünchenPart 3 : Munich, Max-PlanckPart 4 : Barcelona, SpainPart 5 : IHES, FrancePart 6 : LPT ENS, FrancePart 7 : IST, PortugalPart 8 : Nordisk Institut for TeoretiskFysikPart 9 : Trinity College, IrelandPart 10 : INFN, ItalyPart 11 : Turin, ItalyPart 12 : Louvain, BelgiumPart 13 : Imperial College, AngleterrePart 14 : Université de Neuchatel,SuissePart 15: Université de Patras, GrecePart 16 : INR, BulgariePart 17: Université d'Utrecht,HollandePart 18: University d'Iceland, IcelandPart 19: Université de Padou, ItaliePart 20: Université de Milan, ItaliePart 21: Université de Bruxelles,BelgiquePart 22: Université d'Edinbourg,EcossePart 23 : ETH, SuissePart 24: Université de Craiova,RoumaniePart 25: Université de Groningen,Hollande

01/11/2004 -30/10/2008

National grants

ANR stands for "Agence nationale de la recherche" since 2005.

ANR Chaire d'excellence

Person Acronym : Topic Dates

R. Britto HSPQCD : Hard Scattering in Precision QCD15/12/200914/11/2012

G. SoyezJets4LHC : Developing new jet algorithms Optimising theirparameters for LHC physics

31/12/201030/12/2013

F. VernizziCMBSecond : Cosmic Microwave Background Anisotropiesat Second Order

01/12/200930/11/2013

ANR JCJC - Jeune chercheur, jeune chercheuse (Young researcher)

Local contact Acronym : Topic Coordinator Dates

I. BenaString-QCD-BH : String Theory,QCD and Black Holes

I. Bena22/07/200831/12/2013

S. LavignacNEUPAC : Propriétés non standarddes neutrinos et leur impact enastrophysique et en cosmologie

C. Volpe(IPN, Orsay)

05/12/200504/12/2008


S. NonnenmacherRESOCHAOQUAN : Résonances etdécohérence en chaos quantique

S. Nonnenmacher30/11/200529/05/2009

S. NonnenmacherMETHCHAOS : Méthodes spectralesen chaos classique et quantique

C. Guillarmou(ENS, Paris)

01/11/200931/10/2013

G. ServantDARKPHYS : Matière noire eténergie noire : un dé pour laphysique des particules

G. Servant06/11/200606/11/2010

ANR Blanc


M. BauerSLE : Outils probabilistes et invarianceconforme en théorie des champs : SLEet autres processus de croissance

D. Bernard(ENS Paris)

06/11/200601/11/2010

F. BernardeauNLDyn : Dynamique gravitationnellenon linéaire en cosmologie

F. Bernardeau05/11/200704/11/2010

G. Biroli

DynHet : Quantative characterisationof dynamic heterogeneities in glassymaterials : models, simulations and newexperiments

F. Ladieu(CEA/SPEC)

08/11/200707/01/2011

G. BiroliFAMOUS : Far from equilibriumphenomena in quantum systems

L. Cugliandolo(UPMC)

01/10/200930/09/2012

B. Eynard GranMA : Large Random MatricesA. Guionnet(ENS Lyon)

01/01/200931/12/2011

T. GarelC. Monthus

POLINTBIO : Polymères, Interfaces etSystèmes Désordonnés : entreMathématiques, Physique et Biologie

G. Giacomin(Math Paris 7)

20052008

E. IancuDe RHIC à LHC : Interactions fortesdans le régime de haute énergie : deRHIC à LHC

E. Iancu06/11/200601/11/2010

D. Kosower QCD@LHC : QCD, torseurs et le LHC D. Kosower06/12/200506/12/2008

S. LavignacTH-EXP@TEV : Confronting theorywith experiments at the Terascale

S. Lavignac20/12/201019/11/2014

R. MinasianBHTSV : Structure of vacuum,topological strings and black holes

R. Minasian06/11/200606/11/2009

J.-Y. Ollitraulthadron@LHC : Hadron phenomenologyin proton-proton and nucleus-nucleuscollisions at the LHC

J.-Y. Ollitrault01/01/200931/12/2012

C. PépinECCE : Extreme conditions correlatedelectrons

D. Braithwaite(CEA Grenoble)

06/11/200606/11/2009

H. Saleur

INT-AdS/CFT : Structures intégrableset la conjecture AdS/CFT : chaînes despin et modèles sigma non-linéairessypersymétriques

H. Saleur06/11/200606/11/2008

H. SaleurDIME : Disorder, interactions,transport in low dimensions : exactmethods and results

H. Saleur20/12/201019/12/2014

C. SavoyPhys@col&cos : Physique au-delà dumodèle standard : implications pour lescollisionneurs et la cosmologie

A. Djouadi(Paris 11)

01/12/200501/12/2008

Appendices 193

ANR Systèmes complexes et modélisation mathématique"


M. BarthélémyDyxi : Dynamiques CitadinesCollectives : Hétérogénéités Spatiales etIndividuelles

J.-P. Nadal(ENS&EHESS)

2009-2012

RTRA

RTRA stands for "Réseau thématique de recherche avancée -Triangle de la Physique du Plateaude Saclay" since 2007.

Person Topic DatesJ.-M. Luck Invitation Y. Avishai 2007

G. BiroliMeeting "Dynamical heterogeneities in glasses, colloids and granularmedia, Leiden (Pays-Bas)"

2007-2008

G. BiroliA. Lefèvre

Beg-Rohu school 2008

H. Orland Invitation D. Andelman 2008V. Pasquier,D. Serban

Les Houches summer school 2008

O. ParcolletAspen conference "Correlated Behavior and Quantum Criticality inHeavy Fermion and Related Systems "

2008-2009

D. Serban 15th Itzykson Meeting "New Trends In Quantum Integrability" 2009-2010V. Pasquier,D. Serban

Conference Physics in the Plane, Les Houches 2010

C. Godrèche 16th Itzkykson Meeting "Extremes and Records" 2010-2011L. Zdeborova starting/installation grant, DySpaN "Dynamics on sparse networks" 2011-2014

Other national and international programs

CEFIPRA stands for Indo French Centre for the Promotion of Advanced Research.COFECUB stands for "Comité Français d'Evaluation de la Coopération Universitaire et Scien-tique avec le Brésil".ECO-NET stands for "Programmes de collaboration avec l'Europe de l'est et l'ex-URSS".ESF stands for European Science Foundation.GDR stands for "Groupement de recherche" of CNRS.GDRI stands for "Groupe de recherche international" of CNRS.GRAM stands for "Gravitation, Références, Astronomie, Métrologie" of CNRS.PEPS stands for "Projets Exploratoires Pluridisciplinaire" of CNRS.PHC stands for "Partenariats Hubert Curien du ministères des Aaires étrangères et européennes,avec le soutien du ministère de l'Enseignement supérieur et de la Recherche".PICS stands for "Projet International de Coopération Scientique" of CNRS.PNCGC stands for "Programme National de Cosmologie et Galaxies" of CNRS.P2I stands for "Groupement d'intérêt scientique Physique des deux innis".

Program Theme Partner Contact Dates

ESFHOLOGRAV "Holographicmethods in strongly coupledsystems""

University ofSouthampton,UKCERNENS

I. BenaG. KorchemskyD. KosowerI. KostovR. PeschanskiD. Serban

2009-2014


PICSAspects of String Theory withuxes

England

I. BenaM. GrañaM. Petrini(coord.)

2010-2012

P2IMatière Noire et NouvellePhysique: une attaque surplusieurs fronts

F. Bernardeau2008-2010

PNCGCalculs de précision pour grandsrelevés cosmologiques

F. Bernardeau2011

PHC SakuraPrecision calculations forcosmological large-scalestructure observations

RESCEU,University ofTokyo

F. Bernardeau 20112012

CNRS-USAProgrammed'échange

Fluctuations et longueur decorrélation dynamiques dans lessystemes vitreux

USA G. Biroli2007-2008

PHC PessoaThe Early Universe and DarkEnergy

Université deLisbonne

P. Brax2010

GRAM

Progress on Old and NewThemes in Cosmology(conference PONT Avignon2011)

P. Brax2011

P2IDes micro interactionsélémentaires aux macrostructures cosmiques et retour

IAP ParisM. Cirelli 2008-2010

PNCG

Progress on Old and NewThemes in Cosmology(conference PONT Avignon2011)

M. Cirelli 2011

PEPS

Decaying Dark Matter, matièrenoire asymétrique et eet del'annihilation de matière noiresur la formation de galaxies

P. Serpico(coord.LAPThAnnecy)M. CirelliF. IoccoG. ServantG. Zaharijas

2010-2011

PHC Jules VernePhysical Applications ofRandom Graph Theory

University ofIceland

F. David20062007

PICSSystemes intégrables discrets,algébres d'amas et positivité

USA P. Di Francesco2011

Echange France -MIT

The Mathematics of LiouvilleQuantum Gravity

MIT-FranceSeed Fund

B. Duplantier01/01/2011-08/31/2012

PEPS SLE & Quantum Gravity B. Duplantier05/01/2010-31/12/2010

COFECUBECOS-SUD

Generalizing Geometry in StringTheory : its phenomenologicalimplications

Argentine

M. GrañaR. MinasianM. Petrini(coord.)

20082012

Echange France -MIT

Generalizing geometry in stringtheory

MIT-FranceSeed Fund

M. GrañaR. Minasian(coord.)

2006-2007

Appendices 195

CNRS-USAProgrammed'échange

Nouvelles approches auprobleme de la brisure desymétrie électrofaire

Cornell, UCDavis

C. Grojean 2006-2008

PHC AmadeusDu RHIC au LHC sur unesupercorde

ViennaUniversity oftechnology(Autriche)

E. Iancu 20092010

COFECUBCapes

Théories eectives et techniquesnon-perturbatives pour dessystèmes de quarks et de gluons

Brasil E. Iancu20092013

CNRS - PICSSymétries cachées desamplitudes de diusion dans lesthéories de Yang-Mills

Russie G. Korchemsky2010

ECO-NETIntégrales de Feynman à deuxboucles et au-delà

SkobeltsynInst. Nucl.Phys.,LomonosovMoscow StateUniv.;ChelkowskiInst. Phys.,Univ. Silesia,Pologne

D. Kosower 20062008

Echange France -MIT

Perturbative amplitudes ingauge theory and quantumgravity

MITD. Kosower -P. Vanhove

20082009

PHC SakuraMatrix Models and StringTheory

Institut Rikende Kyoto(Japan)

I. Kostov20062007

PHC RilaGéométrie aléatoire, gravitéquantique et théories conformes

Institut derecherchenucléaire etde l'énergienucléaire,Soa(Bulgarie)

I. Kostov20072008

GDRIFrench-Russian network inTheoretical and MathematicalPhysics

Académie desSciencesRusse

I. KostovJ.-M. Maillet(coord.)V. Terras(coord.)

2008-2012

PHC ProteusPhysics from the grandunication scale to LHCenergies

Slovenia S. Lavignac20102011

GDR Quantum Dynamics

S.Nonnenmacher(coord.) - S.DeBièvre (Lille) -Alain Joye(Grenoble)

20092012

COFECUB USPLes premiers instants d'unecollision d'ions lourdsultra-relativistes

Brasil J.-Y. Ollitrault20082011


CEFIPRAHot and dense matter inquantum chromodynamics

LPT Orsay;TIFRMumbai;VECCKolkata

J.-Y. Ollitrault20052007

CEFIPRA Extreme QCD in the LHC eraTIFRMumbai

J.-Y. Ollitrault20112013

PHC Polonium QGP and StringsJagellonianUniversity(Pologne)

R. Peschanski 20082009

ESF

Interdisciplinary Statistical andField Theory Approaches toNanophysics and LowDimensional Systems(INSTANS)

H. Saleur

01/05/2005-30/04/2010

COFECUBCapes

La frontière des hautes énergies:exploration des nouveauxmodèles de la physique desparticules au collisionneur LHCdu CERN et aux expériencesavec des neutrinos

Brasil C. Savoy2007-2009

Coopérationscientique etuniversitaire

Hidden structures of gauge andquantum gravity amplitudes

Institut NielsBohr,Copenhague

P. Vanhove2010

ESF "L'Univers quasi-Gaussian" F. Vernizzi 2009

Appendices 197

D.4 Habilitation thesis - Habilitation à diriger des recherchesBena Iosif

Black Holes, Black Rings and their Microstates (Trous noirs, anneaux noirs et leur microé-tats) [t09/347],Université Pierre et Marie Curie - Paris 6, Spécialité : Physique, 16/06/2009.

Nonnenmacher StéphaneA few aspects of quantum chaos (Quelques aspects de chaos quantique) [t09/127],Université Paris-Sud 11, Spécialité : Mathématiques (option Physique Mathématique),05/06/2009.

Pépin CatherineQuantum critical points in strongly correlated electron compounds (Points critiques quan-tiques dans les composés à fortes corrélations électroniques) [t08/315],Université Pierre et Marie Curie - Paris 6, Spécialité : Physique Théorique, 06/11/2008.

Serban DidinaIntegrability and the AdS/CFT correspondence (Intégrabilité et correspondance AdS/CFT)[t10/042],Université Paris-Sud 11, Spécialité : Physique Théorique, 29/05/2009.

Valageas PatrickFormation of large-scale structures in cosmology: gravitational dynamics (Formation desstructures de grande échelle en cosmologie: dynamique gravitationnelle) [t10/203],Université Paris Diderot - Paris 7, Spécialité : Astrophysique, 03/12/2010.

Vanhove PierreNon-renormalisation theorems in string theory (Théorèmes de non-renormalisation en théoriedes cordes) [t07/063],Université Pierre et Marie Curie - Paris 6, Spécialité : Physique Théorique, 26/10/2007.








D.5 Doctoral schools - Écoles doctoralesIPhT is aliated to 3 écoles doctorales:

ED 107 École doctorale de physique de la région parisienne.

ED 447 (alias EDX) École doctorale de l'École polytechnique.

ED 517 PNC - Particules, Noyaux et Cosmos (formerly ED 381: Constituants élémentaires etsystèmes complexes).

Appendices 199

D.6 PhD defensesBetween June 2007 and May 2011, 21 PhD theses have been defensed at IPhT:

Hosteins PierreNeutrino masses and physics beyond the standard model (Masse des neutrinos et physiqueau-delà du modèle standard) [t07/200],supervised by S. Lavignac, Université Paris-Sud 11, ED 381, 10/09/2007.

Orantin NicolasFrom matrix model's topological expansion to topological string theories: counting surfaceswith algebraic geometry (Du développement topologique des modèles de matrices à la théoriedes cordes topologiques : combinatoire de surfaces par la géométrie algébrique) [t07/119],supervised by B. Eynard, Université Pierre et Marie Curie - Paris 6, ED 107, 13/09/2007.

Ikhlef YacineExact results on two-dimensional loop models (Résultats exacts sur les modèles de boucles endeux dimensions) [t07/216],supervised by H. Saleur and J. Jacobsen, Université Paris-Sud 11, ED 107, 27/09/2007.

Andreanov AlexeiGlass transition: a mean-eld theory (Transition vitreuse: théorie de champ moyen) [t07/201],supervised by G. Biroli and J.-P. Bouchaud (CEA-Spec), École Polytechnique, ED 447,09/10/2007.

Vergu CristianTwistors, strings and supersymmetric gauge theories (Twisteurs, cordes et théories de jaugesupersymétriques) [t08/120],supervised by D. Kosower, Université Pierre et Marie Curie - Paris 6, ED 107, 15/07/2008.

Delaunay CédricElectroweak symmetry breaking: origin and consequences (Brisure de symétrie électrofaible :origine et conséquences) [t08/238],supervised by C. Grojean, Université Paris-Sud 11, ED 107, 02/10/2008.

Candu ConstantinDiscretisation of conformal sigma models on superspheres and projective superspaces (Dis-crétisation des modèles sigma invariants conformes sur des supersphères et superespaces pro-jectifs) [t08/237],supervised by H. Saleur, Université Pierre et Marie Curie - Paris 6, ED 107, 31/10/2008.

Michel YannProperties of extremal black holes in supergravity and string theory (Aspect des trous noirsextrémaux en supergravité et en théorie des cordes),supervised by P. Vanhove and B. Pioline, Université Pierre et Marie Curie - Paris 6, ED 107,01/12/2008.

Beuf GuillaumeContributions to the study of strong interactions at high energy and high density (Contribu-tions à l'étude des interactions fortes à haute énergie et haute densité) [t09/314],supervised by R. Peschanski, Université Pierre et Marie Curie - Paris 6, ED 107, 26/06/2009.

Bon MichaëlPrediction of secondary structures of RNA with pseudoknots (Prédiction de structures sec-ondaires d'ARN avec pseudo-noeuds) [t09/256],supervised by H. Orland, École Polytechnique, ED 447, 21/09/2009.

Prolhac SylvainExact results for the asymmetric simple exclusion process (Méthodes exactes pour le modèled'exclusion asymétrique) [t09/161],supervised by K. Mallick, Université Pierre et Marie Curie - Paris 6, ED 107, 23/09/2009.












Volin DmytroQuantum integrability and functional equations (Intégrabilité quantique et équations fonction-nelles) [t09/283],supervised by I. Kostov and D. Serban, Université Paris-Sud 11, ED 107, 25/09/2009.

Benlagra AdelQuantum criticality in 3He bi layers and heavy fermion compounds (Criticalité quantique dansles bi-couches d' 3He et les composés à fermions lourds) [t09/274],supervised by C. Pépin, Université Paris-Sud 11, ED 107, 09/11/2009.

Sarlat ThomasA nite dimensional model for the glass transition (Un modèle de dimension nie pour latransition vitreuse) [t09/296],supervised by A. Billoire, Université Pierre et Marie Curie - Paris 6, ED 107, 13/11/2009.

Schenck EmmanuelOpen quantum systems and semiclassical methods (Systèmes quantiques ouverts et méthodessemi-classiques) [t09/266],supervised by S. Nonnenmacher and A. Voros, Université Pierre et Marie Curie - Paris 6, ED107, 17/11/2009.

Ruef ClémentBlack holes in string theory: towards an understanding of quantum gravity (Trous noirs enthéorie des cordes : vers une compréhension de la gravité quantique) [t10/083],supervised by I. Bena, Université Paris-Sud 11, ED 107, 18/06/2010.

Bourgine Jean-ÉmileMatrix models and boundary problems in Liouville gravity (Modèles de matrices et problèmesde bord dans la gravité de Liouville) [t10/168],supervised by I. Kostov, Université Paris-Sud 11, ED 107, 18/06/2010.

Gombeaud ClémentThermalization in ultrarelativistic heavy ion collisions (Thermalisation dans les collisionsd'ions lourds ultrarelativistes) [t10/199],supervised by J.-Y. Ollitrault, Université Pierre et Marie Curie - Paris 6, ED 107, 02/07/2010.

Dubail JérômeBoundary conditions in some non-unitary conformal eld theories (Conditions aux bords dansdes théories conformes non unitaires) [t10/198],supervised by H. Saleur and J. Jacobsen, Université Paris-Sud 11, ED 107, 07/09/2010.

Messio LauraGround states and excitations of frustrated magnetic systems, from the classical limit tothe quantum case (Etats fondamentaux et excitations de systèmes magnétiques frustrés, duclassique au quantique) [t10/144],supervised by G. Misguich and C. Lhuillier (LPTMC-UPMC), Université Pierre et MarieCurie - Paris 6, ED 389, 14/09/2010.

Marchal Olivier(Aspects géométriques et intégrables des modèles de matrices aléatoires) [t10/200],supervised by B. Eynard and J. Harnad (Montreal), Université Paris Diderot - Paris 7, ED107, 20/12/2010.











Appendices 201

D.7 Current PhD studentsIn May 2011, IPhT has 21 PhD students:

Parmentier JeannePhenomenological aspects of supersymmetry breaking (Aspects phénoménologiques de la bri-sure de supersymétrie),supervised by S. Lavignac and E. Dudas (X-CPhT), 200711/07/2011.

Borot GaëtanSome problems in enumerative geometry, random matrices, integrability, studied via geometryon Riemann surfaces (Quelques problèmes de géométrie énumérative, de matrices aléatoires,d'intégrabilité, étudiés via la géométrie des surfaces de Riemann),supervised by B. Eynard, 200823/06/2011.

Cluzel ÉmelineInation in string cosmology (Ination en cosmologie des cordes),supervised by P. Brax and J. Martin (IAP), 200822/09/2011.

Giecold GrégoryGauge/String duality and eld theories at strong coupling (Correspondance AdS/CFT, sesextensions et applications aux théories de champs à fort couplage),supervised by I. Bena and E. Iancu, 200817/06/2011.

Goi EnricoAspects of supersymmetry breaking in type IIA superstring theory: vacua and deformations(Quelques aspects de la brisure de supersymétrie en théorie des cordes de type IIA: vides etdéformations),supervised by R. Minasian, 200821/09/2011.

Grandclaude HélèneDynamics of out-of-equilibrium networks (Dynamique des réseaux hors-équilibre),supervised by C. Godrèche, 20082011.

Mariadassou SophiePreheating after small eld ination (Phase de préchauement après l'ination à petit champ),supervised by P. Brax, 20082011.

Orsi FrancescoFlux Compactications in String Theory (Compactications avec ux en théorie des cordes),supervised by M. Grana, 20082011.

Stephan Jean-MarieEntanglement in low-dimensional quantum systems (Intrication dans des systèmes quantiquesà basse dimension),supervised by V. Pasquier, 20082011.

Bondesan RobertoSupersymmetric eld theory and statistical mechanics models (Théorie de champs super-symétrique et mécanique statistique),supervised by H. Saleur and J. Jacobsen, 20092012.

Peng ZongrenTopics in N=4 Yang-Mills theory (Sujets dans la théorie de Yang-Mills N=4),supervised by D. Kosower, 20092012.

Sciolla BrunoOut-of-equilibrium quantum dynamics for cold atoms (Dynamique quantique hors-équilibrepour atomes froids),supervised by G. Biroli, 20092012.


Shenderovich IgorIntegrable structures in gauge theories and supersymmetric string theories (Structures inté-grables dans les théories de jauge et dans les théories des cordes supersymétriques),supervised by I. Kostov and D. Serban, 20092012.

Van de Rijt NicolasSignatures of the primordial universe in large scale surveys (Signatures de l'univers primordialdans les grands relevés cosmologiques),supervised by F. Bernardeau and F. Vernizzi, 20092012.

Laidet JulienQCD's evolution equations in saturated regime (Équations d'évolution en QCD en régimesaturé),supervised by F. Gelis and E. Iancu, 20102013.

Lazarescu AlexandreFinite size results for the open asymmetric exclusion process (Le processus d'exclusion asymé-trique ouvert: quelques résultats en taille nie),supervised by K. Mallick, 20102013.

Massai StefanoNon-supersymmetric compactications of string theory (Compactications non supersymé-triques de la théorie des cordes),supervised by M. Grana, 20102013.

Puhm AndreaBlack holes in string theory (Trous noirs en théorie de cordes),supervised by I. Bena, 20102013.

Tourkine PiotrUV completeness of quantum gravity theories (Complétude ultraviolette des théories de gravitéquantique),supervised by P. Vanhove, 20102013.

Vasseur RomainField Theory and non-interacting fermionic systems with quenched disorder (Théorie deschamps et systèmes d'électrons libres désordonnés),supervised by H. Saleur and J. Jacobsen, 20102013.

Appendices 203

D.8 Postdocs

Name Supervisor OriginFinancialSupport

Dates

ALBACETE LOPEZJavier

E. Iancu ECT, TrentoMarie CurieIEF

june-09 may-12

ALEXANDROVAlexander

B. Eynard Imperial College ANR oct-09 sept-11

ALMEIDA Leandro R. Britto Univ. New York ANR sept-10 sept-12AVSAR Emil E. Iancu Univ. De Lunds ANR dec-07 oct-09AYYER Arvind K. Mallick Rutgers Univ. CEA oct-08 sept-10BADGER Simon D. Kosower Univ. Durham ANR oct-06 sept-08

BENA Cristina H. Saleur Rutgers Univ.Marie CurieIEF

oct-06 oct-08

BON Michael H. Orland IPhT CEA mar-11 feb-12

BONVIN Camille F. BernardeauDep. Physique théorique,Genève

CEA P2I oct-08 sept-10

BOWICK Marc John E. Guitter Univ. Syracuse EGIDE jan-07 jul-07

CAMMAROTAChiara

G. Biroli Univ. RomeANR -CNRS -CEA

nov-09 nov-12

CAPRINI Chiara P. Brax Univ. Geneve ANRoct-07 perma-nent

CHESTERMANMichael

P. Vanhove Karlstad University CEA oct-05 sept-07

CIRELLI Marco C. Savoy Yale Univ.EGIDE -CEA

sept-06 perma-nent

DIANA Giovani D. Kosower INFN Milan ERC dec-10 nov-12DE SANDESKIMURA Horoshi

C. Savoy Univ. Sao Paulo COFECUB oct-10 mar-12

DESROSIERS Patrick B. Eynard Melbourne Univ. CEA sept-07 feb-08

EL-SHOWK Sheer I. Bena Univ. AmsterdamRUBICON -ERC

sept-09 sept-13

FERRERO Michel O. Parcollet CPHT, Polytechnique ANR oct-08 sept-09

FRIGERIO Michele S. Lavignac Univ. of CaliforniaMarie CurieEIF

sept-07 aug-09

GAYNUTDINOVAzat

H. Saleur Inst. Lebedev, MoscowCEA - MarieCurie

sept-09 oct-13

GIUSTO Stefano I. Bena Univ. Toronto CEA sept-07 aug-09GROMOV Nikolay H. Saleur ENS Paris ANR nov-07 nov-08GUICA Monica-Maria I. Bena LPTHE Jussieu ANR sept-10 aug-11HALMAGYI Nick I. Bena Univ. Chicago ANR sept-08 aug-11

HATTA Yoshitaka E. IancuRIKEN BNL ResearchCenter

CEA oct-06 jan-08

HIDALGO Irene S. Lavignac Orsay ANR nov-07 feb-08HOSOMICHI Kazuo I. Kostov Univ. Toronto CEA oct-05 sept-07

HUANG Zhiqi F. Vernizzi Univ. TorontoANR -Eurotalents

oct-10 sept-13

IOCCO Fabio M. CirelliINAF, Observatoire,Florence

CEA P2I nov-08 oct-09

JOHANSSON Henrik D. Kosower UCLA - Los Angeles ERC oct-09 oct-12KASHANI-POORAmir-Kian

R. Minasian Univ. Amsterdam ANR oct-08 oct-09

KIM Ki-Seok C. Pepin KIAS Seoul ANR sept-07 aug-08


KUGERATSKISOUSA Maria

E. Iancu Univ. Sao Paulo COFECUB june-07 june-08

KYTOLA Kalle F. David Univ. of HelsinkiMarie CurieRTN

nov-06 nov-07

LAPPI Tuomas F. GelisBrookhaven NationalLaboratory, Upton

CEA oct-07 dec-09

LUZUM Matt J.-Y. Ollitrault Univ. Washington Seattle ANR - ERC oct-09 sept-12MANSCHOT Ian I. Bena Rutgers Univ. ANR - CEA sept-09 sept-11

MARQUET Cyrille IPhTMarie CurieOIF

sept-07 aug-10

MARQUES Diego M. GranaUniv. De La Plata,Argentine

ERC apr-11 may-12

MIRABELLAEdouardo

R. Britto Max Planck Inst. ERC oct-09 sept-11

NO Jose Miguel S. Lavignac IFT, MadridCEA -Eurotalents

oct-09 sept-11

PORTUGAL Licinio E. Iancu Univ. Rio de Janeiro COFECUB sept-06 dec-07

RAY Tirtha Sankar S. LavignacSaha Inst. Of NuclearPhysics

ITN - CEA jul-10 june-12

SAUERESSIG Frank R. Minasian Utrecht Univ. ANR sept-07 sept-08

SAUSSET Francois G.BiroliUniv. Pierre et MarieCurie

bourse nov-08 oct-09

SAXENA Ashish I. Bena Univ. TorontoMarie CurieIRG

sept-07 feb-08

SEFUSATTI Emiliano F. BernardeauFermi NationalAccelerator Lab.

ANR - MarieCurie IEF

jan-09 jan-12

SIL Arunansu C. Savoy Univ of DelawareMarie CurieITN

oct-06 sept-09

TARZIA Marco G. Biroli Univ. Orsay CNRS dec-07 nov-08TRIENDL Hagen I. Bena Univ. Hambourg ANR oct-10 sept-12VERCNOCKE Bert I. Bena Univ. Leuwen ERC oct-10 sept-12VICEDO Benoit H. Saleur Univ. Cambridge ANR sept-08 aug-10WYNANTS Bram H. Orland Univ. Leuwen CEA oct-10 sept-11ZAHARIJAS-SEFUSATTIGabrijela

G. Servant Univ. StockholmANR - CEA- P2I

nov-09 oct-11

ZAMPONI Francesco G. Biroli LPT, Paris CEA sept-06 aug-07

Appendices 205

D.9 Internships

Supervisor Student Level DatesP. Vanhove Valentin Assassi Ecole Centrale Paris 01/09/2010-31/12/2010B. Eynard Antoine Baker Ecole Normale Supérieure 20/02/2007- 27/07/2007E. Sefusatti Nicolas Bonne Polytechnique 06/04/2011-29/06/2011C. Caprini Simon Bonnefoy Univ. Montpellier 04/03/2011-15/06/2011

B. EynardGuillaumeBoudarham

Univ. Pierre et Marie Curie 15/01/2007-05/03/2007

M. CirelliCarolinBraüninger

Univ. Tubingen 13/10/2008-14/04/2009

E. Iancu Clémentine Broutin Polytechnique 10/04/2007-06/07/2007R. Britto Xavier Busch Polytechnique 13/10/2008-13/04/2009F. Bernardeau Sandrine Codis ENS Paris 10/01/2011-04/03/2011G. Soyez Stéphane Dartois ENS Lyon 20/04/2011-01/08/2011K. Mallick Alban Debacker ESPCI Paris Tech 01/07/2009-31/07/2009F. Gelis Thomas Epelbaum ENSTA Paris 06/04/2010-06/08/2010F. Gelis Thomas Epelbaum M2 physique théorique 01/01/2011-28/02/2011S. Nonnenmacher Quentin Gendron ENS Cachan 02/06/2009-31/07/2009

P. BraxSophieGrezes-Rueff

Univ. Orsay 07/05/2007-20/06/2007

J. Bros Emmanuel Jolibois ENS Paris 06/02/2008-14/03/2008G. Korchemsky Andrey Lokhov Polytechnique 12/04/2010-23/07/2010G. Korchemsky Andrey Lokhov Polytechnique 10/01/2011-04/03/2011L. Zdeborova Jared Lolli ENS Paris 01/02/2011-30/06/2011M. Barthelemy Jacopo Nespolo Univ. Paris VI 12/01/2010-05/03/2010R. Britto Adrien Nicolas Polytechnique 12/04/2010-31/07/2010I. Kostov Amael Obliger Univ. Paris 7 17/01/2011-20/05/2011J.-P. Blaizot Leticia Palhares PhD, Rio de Janeiro 01/09/2010-31/08/2011M. Cirelli Paolo Panci PhD, Univ. L'Aquila, Italy 15/01/2009-15/07/2009

G. MisguichThiago PenteadoSabetta

Polytechnique 10/01/2011-09/05/2011

C. Pépin Adam Rançon ENS Paris 05/01/2009-26/04/2009P. Brax Benoît Schmauch Polytechnique 11/04/2011-01/07/2011I. Kostov Igor Shenderovich Univ. St Petersburg 01/04/2009-30/09/2009G. Misguich Jean-Marie Stephan M2 physique quantique 01/12/2007-30/04/2008

P. Valageas Julien VandeportalM2 physique chimieMontpellier

10/02/2007-10/07/2007

C. Cataldi Célia Zaffanella Lycée Gustave Eiel 02/10/2007-31/10/2009


D.10 IPhT lecturesThese courses take place Friday morning at IPhT. Most of them are part of the PhD program ofthe ED 107 École doctorale de physique de la région parisienne. They are mainly intended forPhD students, but they are open for everybody. More details are given on the IPhT web site.

Viennot Xavier (LaBRI, Bordeaux)Eléments de combinatoire algébrique; 12 h; Sep 2007.

Bernardeau Francis (IPhT)Cosmologie et uctuations primordiales; 12 h; Nov 2007.

Fayet Pierre (LPT, ENS Paris)Le modèle standard supersymétrique; 12 h; Jan 2008.

Biroli Giulio (IPhT)Transition vitreuse et systèmes hors d'équilibre; 12 h; Mar 2008.

Douçot Benoît (LPTHE, Paris 6-7)Cohérence quantique de systèmes macroscopiques; 12 h; May 2008.

Wiegmann Paul (Chicago Univ.)Hydrodynamic instabilities in quantum liquids; 6 h; Sep 2008.

Saleur Hubert (IPhT)Théorie des champs à basse dimension : introduction et applications; 16 h; Oct 2008.

Deruelle Nathalie (APC, Paris 7)Les trous noirs en relativité générale; 12 h; Jan 2009.

Bauer Michel (IPhT and LPT-ENS Paris)Probabilités et processus stochastiques, pour les physiciens (et les curieux); 12 h; Mar 2009.

Mallick Kirone (IPhT)Développements récents en mécanique statistique loin de l'équilibre; 8 h; May 2009.

Houdayer Jérôme (IPhT)Ondelettes et analyse numérique; 10 h; Jun 2009.

Nonnenmacher Stéphane (IPhT)Chaotic dynamical systems; 12 h; Sep 2009.

Parcollet Olivier (IPhT)Quantum many body problem: selected topics; 10 h; Nov 2009.

Barthélemy Marc (IPhT)Dynamical processes on complex networks; 8 h; Jan 2010.

Petrini Michela (LPTHE, Paris 6)The AdS/CFT correspondence; 10 h; Mar 2010.

Shifman Mikhai (Minnesota Univ. and Chaire Blaise Pascal) andYung Alexei V. (PNPI, S. Petersburg)

Dynamics of supersymmetric gauge theories; 12 h; May 2010.

Peschanski Robi (IPhT) andJanik Romuald (Jagellonian Univ., Krakow)

The dynamics of quark-gluon plasma and AdS/CFT correspondence; 8 h; Nov 2010.

Britto Ruth (IPhT)Introduction to scattering amplitudes; 8 h; Jan 2011.

Durrer Ruth (Geneva Univ.)Cosmology and the cosmic microwave background; 12 h; Mar 2011.

Appendices 207

Kempe Julia (LRI, Paris 11)Quantum algorithms and information; 6 h; Apr 2011.

Zia Royce (Virginia Tech.)Exploring nonequilibrium statistical mechanics with driven diusive systems; 6 h; May 2011.


D.11 Teaching in university or grandes écolesIn french universities, the undergraduate studies (License) last three years, L1, L2 and L3; themaster lasts two years, M1 and M2; nally, the PhD lasts generally three years.

Bauer Michel M1; École normale supérieureIntroduction to quantum eld theory; 30 h/year; 20072011.

Bauer Michel M2; École normale supérieureProbability and stochastic processes for physicists; 45 h/year; 2011.

Bernardeau Francis L3; École polytechniqueGeneral physics, special relativity and quantum physics; 64 h/year; 20082011.

Biroli Giulio M1; École polytechniqueQuantum mechanics and statistical physics; 72 h; 2011.

Blaizot Jean-Paul graduate; University of TokyoQuantum elds at nite temperature: from tera to nano Kelvin; 15 h; 2009.

Blaizot Jean-Paul graduate; University of Nanjing (China)Quantum elds at nite temperature: from tera to nano Kelvin; 15 h; 2011.

Bouttier Jérémie L3; ESPCIMathematical methods for physicists; 24 h/year; since 2009.

Britto Ruth M1/M2; EPFL LausanneConstructing scattering amplitudes; 14 h; 2010.

David François M2; ENS ParisIntroduction to statistical eld theory; 40 h/year; 2007 2011.

David François M2; Perimeter Institute, Waterloo, CanadaPerimeter scholar international program; quantum eld theory II; 20 h/year; 2009, 2010.

Di Francesco Philippe Graduate; Univ. Illinois, Urbana-ChampaignIntegrable combinatorics; 45 h; 2009.

Duplantier Bertrand M1; École polytechniquePhysics of polymers and biological membranes; 36 h; 2008.

Duplantier Bertrand M2; EPFL, LausanneThe polymer physics of DNA; 16 h; 2009.

Gelis François M2; Université Paris-Sud 11, M2 NPACIntroduction to the physics of heavy ion collisions; 6 h/year; 2008 2011.

Grojean Christophe M2; EPFL LausanneIntroduction to SM; 39 h; 2011.

Kosower David PhD; Weizmann Institute, IsraelOn-shell methods in gauge eld theory; 12 h; 2010.

Lavignac Stéphane M2; ENSExercises in gauge theory of electroweak interactions; 12 h/year; 2008 2011.

Mallick Kirone L3; ESPCIMéthodes mathématiques pour la physique; 22 h; 2007.

Minasian Ruben M2; ENS ParisGeometrical methods of theoretical physics; 39 h/year; 2007 2011.

Ollitrault Jean-Yves L3, M1; École polytechniqueQuantum physics, statistical mechanics, particle physics; 64 h/year; 2007 2011.

Appendices 209

Soyez Grégory M2; ENSExercises in quantum chromodynamics; 8 h; 2011.

Vanhove Pierre PhD; IHESPerturbative quantum gravity; 20 h; 2011.

Zdeborova Lenka M1, M2, PhD; Tokyo Institute of Technology, JapanStatistical physics on random graphs; 9 h; 2010.

Zdeborova Lenka M1; ESPCI, ParisTutorials in statistical physics; 16 h/year; 2007, 2008.


D.12 Teaching in summer schoolsBauer Michel A short introduction to critical interfaces in 2d;

4 h; in School on stochastic geometry, the stochastic Loewner evolution, and non-equilibriumgrowth processes; Trieste; July 2008.

Bauer Michel A short introduction to critical interfaces in 2d;4 h; in Modern applications of conformal invariance, topical school in statistical physics;Nancy; March 2011.

Biroli Giulio Statistical dynamics;13.5 h; in Beg Rohu summer school 2010; Beg Rohu; Aug 2010.

Britto Ruth Scattering amplitudes in gauge theories;14 h; in Dutch research school of theoretical physics; Driebergen, NL; Feb 2010.

Britto Ruth Multi-leg amplitudes;3 h; in Spring course of the international graduate school Bielefeld-Paris-Helsinki; Orsay;Mar 2010.

Britto Ruth Recursive construction of amplitudes;6 h; in Summer school on the structure of local quantum elds; Les Houches; Jun 2010.

Cirelli Marco Dark matter;2 h; in Universenet summer school and meeting; Barcelona, Spain; Sep 2009.

Cirelli Marco Hoping to indirectly detect dark matter with cosmic rays;3 h; in Carpathian summer school of physics; Sinaia, Romania; Jun 2010.

Cirelli Marco Dark matter indirect detection;1 h; in Universenet summer school and meeting; Lecce, Italy; Sep 2010.

David François Quantum eld theory and renormalisation group;20 h; in Summer school of mathematical physics; Shanghai institute of advanced studies,Shanghai, China; Aug 2009.

Di Francesco Philippe Integrable combinatorics: from loop gas to orbital varieties and be-yond;3 h; in Random trees 2007; Univ. Reykjavik, Iceland, ; Aug 2007.

Di Francesco Philippe Combinatorics;3 h; in European network ENIGMA school Quantum integrability; La Londe les Maures,France; Oct 2007.

Di Francesco Philippe Integrable combinatorics;15 h; in Oberwolfach seminar Enumerative combinatorics and integrable models of statisticalmechanics; Mathematisches Forschungsinstitut Oberwolfach; Nov 2007.

Di Francesco Philippe Integrable models of statistical physics and enumerative combina-torics;13 h; in Combinatorics and statistical mechanics; Erwin Schrödinger international institutefor mathematical physics, Vienna, Austria; Jul 2008.

Di Francesco Philippe Integrable combinatorics;16 h; in Semester Statistical physics, combinatorics and probability: from discrete to contin-uous models; Institut Henri Poincaré, Paris; fall 2009.

Di Francesco Philippe Master class: cluster algebras;4 h; in Center for quantum geometry of moduli spaces; Aarhus Univ., Denmark; Jun 2010.

Di Francesco Philippe Integrable combinatorics;6 h; in Clay mathematics institute 2010 summer school Probability and statistical physics intwo and more dimensions; Buzios, Brazil; Jul 2010.

Appendices 211

Duplantier Bertrand A rigorous perspective on Liouville quantum gravity and the KPZ re-lation;1.5 h; in Exact methods in low-dimensional statistical physics and quantum computing; LesHouches; Jul 2008.

Eynard Bertrand Symplectic invariants of spectral curves and their applications to enumera-tive geometry;6 h; in From integrable structures to topological strings and back; Sissa, Trieste; Sep 2008.

Eynard Bertrand Symplectic invariants of spectral curves and their applications to enumera-tive geometry;5 h; in A new recursion from random matrices and topological string theory; IPMU Tokyo;Dec 2008.

Eynard Bertrand Enumeration of maps;5 h; in Statcomb school on embedded random graphs; IHP, Paris; Autumn 2009.

Eynard Bertrand Matrix models for topological strings;5 h; in Trimester matrix models and geometry CAMGSD thematic period; IST Lisbon; Au-tumn 2009.

Eynard Bertrand From matrix models to algebraic geometry;4 h; in From matrix models to algebraic geometry; Northeastern, Boston; Oct 2010.

Gelis François Gluon saturation from DIS to nucleus-nucleus collisions;3 h; in School on QCD, low-x physics, saturation and diraction; Copanello, Italy; Jul 2007.

Gelis François Pre-equilibrium dynamics in heavy ion collisions;6 h; in Advanced school on QGP; Indian institute of technology, Mumbai, India; Jul 2007.

Gelis François Quantum chromo-dynamics at nite temperature;4.5 h; in 2nd Rio-Saclay meeting; CBPF, Rio de Janeiro, Brazil; Sep 2007.

Gelis François Gluon saturation from DIS to AA collisions;6 h; in Hadronic collisions at the LHC and QCD at high density; Les Houches, France; Apr2008.

Gelis François Color glass condensate and initial stages of heavy-ion collisions;3 h; in Nuclear astrophysics and heavy ion collisions; Dubna, Russia; Jul 2008.

Gelis François Initial conditions in AA collisions;3 h; in Initial conditions in heavy ion collisions collisions; Goa, India; Sep 2008.

Gelis François Introduction to perturbative QCD;3 h; in Aspects of perturbative QCD; Orsay, France; Mar 2010.

Grojean Christophe Alternate electroweak scenarios;3h45; in From string to LHC; Fireies Ashram, Bangalore, India; Dec 2007.

Grojean Christophe Beyond the Higgs: new ideas on electroweak symmetry breaking;6 h; in Third graduate school in physics at colliders: from twistors to Monte Carlos; Turin,Italy; Jan 2008.

Grojean Christophe Beyond the Higgs: new ideas on electroweak symmetry breaking;3 h; in IPM international school and workshop on electroweak physics; Teheran, Iran; May2008.

Grojean Christophe Beyond the Higgs: new ideas on electroweak symmetry breaking;4h30; in Ecole de Gif 2008; Ecole Polytechnique, France; Sep 2008.

http://theory.tifr.res.in/stringslhc/

http://personalpages.to.infn.it/~maina/scuola08/program_2008.html

http://physics.ipm.ac.ir/conferences/ipmep/index.jsp

http://polywww.in2p3.fr/actualites/congres/gif2008/index.php


Grojean Christophe Beyond the standard model at the LHC: new ideas on electroweak sym-metry breaking;2 h; in VII latin american symposium on high energy physics (SILAFAE) + IX Argentinesymposium of particles and elds (SAPyC); Bariloche, Argentina; Jan 2009.

Grojean Christophe Electroweak symmetry breaking: to Higgs or not to Higgs ;3 h; in CERN academic training; CERN, Switzerland; Feb 2009.

Grojean Christophe Beyond the Higgs;4 h; in Ecole de physique des particules et cosmologie; Oran, Algeria; May 2009.

Grojean Christophe Beyond the standard model: the LHC reach;4h30; in The XIV LNF spring school "Bruno Touschek" in nuclear, subnuclear and astropar-ticle physics; Frascati, Italy; May 2009.

Grojean Christophe Beyond the standard model;5 h; in Fourth graduate school in physics at colliders: on the eve of the LHC; Turin, Italy;Jul 2009.

Grojean Christophe Extra dimensions for TeV physics;4h30; in Parma international school of theoretical physics; Parma, Italy; Sep 2009.

Grojean Christophe New physics at the LHC;2 h; in Particle, astrophysics and cosmology winter school; Sesimbra, Portugal; Dec 2009.

Grojean Christophe Electroweak symmetry breaking;1h30; in PSI summerschool on particle physics: Gearing up for LHC physics; Zuoz, Switzer-land; Aug 2010.

Grojean Christophe Beyond the standard model;4 h; in German particle physics school; Maria Laach, Germany; Sep 2010.

Grojean Christophe Electroweak symmetry breaking;2 h; in Second school on the LHC physics; Islamabad, Pakistan; May 2010.

Iancu Edmond Non-linear evolution in QCD at high energies;4.5 h; in Summer School on high-energy QCD, low-x physics, saturation and diraction;Copannello, Italy; Jul 2007.

Iancu Edmond High-energy QCD : the color glass condensate;3 h; in 2nd Rio-Saclay meeting; CBPF, Rio de Janeiro, Bresil; Sep 2007.

Iancu Edmond Gluon saturation and the color glass condensate;6 h; in Winter school on hadronic collisions at the LHC and QCD at high density; LesHouches; Mar 2008.

Iancu Edmond Partons and jets in a strongly-coupled plasma from AdS/CFT;4.5 h; in 48th Cracow school of theoretical physics: aspects of duality; Zakopane, Poland; Jun2008.

Iancu Edmond High energy scattering : from weak to strong coupling;3 h; in First high energy physics school; Magurele, Roumanie; Oct 2008.

Kosower David On-shell methods in gauge eld theory;4.5 h; in String theory - from theory to experiment; Weizmann Institute, Israel; Apr 2008.

Kosower David On-shell methods in gauge theory;4.5 h; in Taiwan Summer Institute; Chi-Tou, Taiwan; Aug 2008.

Kostov Ivan Boundary loop models and 2D quantum gravity;3 h; in Exact methods in low-dimensional statistical physics and quantum computing; LesHouches; Jul 2008.

http://particulas.cnea.gov.ar/workshops/silafae/

http://particulas.cnea.gov.ar/workshops/silafae/

http://indico.cern.ch/conferenceDisplay.py?confId=47260

http://www.lnf.infn.it/conference/lnfss/09/

http://www.lnf.infn.it/conference/lnfss/09/

http://www.ph.unito.it/dft/scuola09/

http://www.pr.infn.it/snft/2009/snft-2009.html

http://pasc.ist.utl.pt/winterschool2009/

http://ltpth.web.psi.ch/zuoz2010/

http://maria-laach.physik.uni-siegen.de/index.php?ID=home

http://indico.ncp.edu.pk/indico/conferenceDisplay.py?confId=6

Appendices 213

Lavignac Stéphane Physics beyond the standard model;3 h; in France-Asia particle physics school (FAPPS); Les Houches; Sep 2008.

Lavignac Stéphane Supersymmetry;6 h; Univ. Catholique de Louvain-la-Neuve, Belgium; Dec 2008.

Mallick Kirone Bethe ansatz and applications to non-equilibrium statistical mechanics;5 h; Tata Institute, Mumbhai, India; Mar 2007.

Mallick Kirone Exact results for the exclusion process;6 h; in ALEA (School of combinatorics and probabilities); CIRM Marseille; Apr 2010.

Misguich Grégoire Quantum spin liquids and fractionalization [t07/161];2 h; in Highly frustrated magnetism; Trieste ICTP, Italy ; Aug 2007.

Misguich Grégoire Quantum spin liquids [t08/250];2 h; in Exact methods in low-dimensional statistical physics and quantum computing; LesHouches; Jul 2008.

Nonnenmacher Stéphane Entropy of chaotic eigenstates;2 h; in Spectrum and dynamics; CRM, Montreal, Canada ; Apr 2008.

Ollitrault Jean-Yves Relativistic hydrodynamics;4 h; in Advanced school on quark-gluon plasma; IIT Mumbai, India; Jul 2007.

Ollitrault Jean-Yves Relativistic hydrodynamics;3 h; in Hadronic collisions at the LHC and QCD at high density; Les Houches; Mar 2008.

Schaeffer Richard Dark energy, dark matter, dark baryons;6 h; in Theoretical physics and mathematics school; Ubu, Brazil; Feb 2010.

Servant Géraldine Introduction to cosmology;2 h; in French physics teachers programme; CERN; Apr 2008.

Servant Géraldine Cosmology and the particle accelerator connection;1 h; in 4th CERN-Fermilab hadron collider physics summer school; CERN; Jun 2009.

Servant Géraldine Introduction to cosmology;2 h; in International physics teachers programme; CERN; Jul 2010.

Servant Géraldine Cosmological consequences of new physics at the TeV scale;1 h; in The Standard Model and beyond-cosmology; Corfu; Sep 2010.

Servant Géraldine Cosmological and astroparticle aspects of physics beyond the StandardModel;3 h; in Annual particle physics retreat; Mainz University; Sep 2010.

Soyez Grégory Phenomenology of hadronic colliders;9 h; in BND school 2010 (Belgian-Dutch-German graduate school in particle physics); Ostend(Belgium); Sep 2010.

Vanhove Pierre Non renormalisation theorems in type II superstrings;2 h; in String theory and the real world, from particle physics to astrophysics; Les Houches;Jul 2007.

Vanhove Pierre Introductory lectures on pure spinor formalism;3 h; in Fundamental aspects of superstring theory; KITP, Santa Barbara, California; Jan2009.

Zdeborova Lenka Probing the energy landscape of random optimization problem;2 h; in Statistical physics of complexity, optimization and biological information; Les Houches;Mar 2010.




D.13 Weekly seminars

Monday 11:00 Mathematical Physics14:00 Statistical Physics

Tuesday 11:00 General SeminarWednesday 14:15 Particle Physics and CosmologyThursday 11:00 Condensed Matter Theory

16:00 PhD seminarFriday 10:00 IPhT lectures

14:15 Matrices, Strings & Random Geometries

Usually, seminars take place in the IPhT seminar room (Claude Itzykson room),which can contain up to 50 persons. For bigger events, we can use in the samebuilding an amphitheater for 150 persons (Amphi Claude Bloch).

IPhT also organizes a condensed matter theory seminar in common with the LPS(Orsay).

Appendices 215

D.14 Claude Itzykson meetings

The Claude Itzykson meetings are the main scientic events at IPhT. Created tohonour the memory of Claude Itzykson and in particular his deep and true love forphysics, they have become a tradition. Every year in June, scientists from all overthe world (mainly but not only physicists) meet for a few days to cover the mainrecent advances on a targeted theme. Two important features are the insistenceon pedagogical seminars and the opportunity given to young researchers as well asestablished experts to give a talk.

Integrability in Gauge and String Theory12th Claude Itzykson Meeting, June 1822, 2007

Organizers: V. Kazakov (LPTENS), I. Kostov, D. Serban.

G. Arutyunov : Zamolodchikov-Faddeev algebra for AdS5×S5 superstringN. Beisert : Symmetries related to AdS/CFT integrabilityN. Berkovits : New limit of the AdS5×S5 sigma modelN. Dorey : Singularities of the magnon S-matrixB. Eden : The BES equation and its strong coupling limitS. Frolov :N. Gromov : Integrability in AdS5×S5 string theory: general 1-loop resultsR. Hernandez : Magnon kinematics in planar N=4 Yang-MillsR. Janik : Wrapping interactions and virtual correctionsG. Korchemsky : Anomalous dimensions of high-spin operators beyond the leading orderD. Kosower : From weak to strong coupling at maximal supersymmetryC. Kristjansen : The strong coupling limit of the scaling function from the quantum string

Bethe ansatzL. Lipatov : BFKL and double-logarithmic resummation for the multi-loop anomalous

dimensions in N=4 SUSYJ. Maldacena : Worldsheets and spin chains with boundaryA. Migdal : Ancient history of conformal eld theoryJ. Minahan : Two loop results for the near at sigma modelA. Rej : Exact results for twist operators in planar N=4 SYMR. Roiban : Probing the higher loop dilatation operator of N=4 SYMK. Sakai : Origin of dressing phase in N=4 Super Yang-MillsH. Saleur : Associative-algebraic approach to logarithmic conformal eld theoriesS. Schafer-Nameki : Quantum integrability in the pure spinor formalismV. Schomerus : Sigma models on superspacesG. Semeno : Finite size giant magnon reduxE. Sokatchev : Conformal properties of N=4 SYM amplitudesM. Staudacher : Transcendentality, dressing, nesting and wrapping in AdS/CFTJ. Teschner : Warm-up for solving noncompact sigma models: the Sinh-Gordon modelA. Tseytiln : Quantum string corrections in AdS5×S5

A. Zabrodin : Hirota equation for supersymmetric spin chainsK. Zarembo : Worldsheet scattering in AdS5×S5

Puzzles of Growth13th Claude Itzykson Meeting, June 911, 2008

Organizers: M. Bauer, D. Bernard (LPTENS), Z. Burda (Univ. Jagiellonski, Krakow), F. David,A. Lefèvre.

E. Ben Jacob : The Mathematical skills of bacteriaF. Camia : Scaling limits of 2D percolationS. Dorogovtsev : Transition from nite- to innite-dimensional treesF. David :M. Drmota : Large random planar graphs


B. Duplantier : Quantum gravity and brownian large deviationsE. Guitter : The three-point function of planar quadrangulationsW. Janke : Percolating excitations - a geometrical view of phase transitionsT. Kennedy : Testing for SLE using the driving processK. Kytölä : Some CFT fusions from SLE local martingalesA. Middleton : Exploring the eects of disorder on geometryA. Okounkov : Noncommutative geometry of planar dimersS. Redner : Cutting cornersH. Saleur : Boundary loop modelsR. Santachiara : Interfaces in lattice Z(N) modelsS. Smirnov : Ising lattice universalityW. Werner : Are frontiers symmetric?

Recent Advances in String Theory14th Claude Itzykson Meeting, June 1719, 2009

Organizers: I. Bena, M. Graña, R. Minasian, P. Vanhove.

O. Aharoni : On d=3 Yang-Mills Chern-Simons theories with fractional branes andtheir gravity duals

N. Arkani-Hamed : Holography and the S-MatrixK. Becker : Torsional heterotic geometriesN. Berkovits : Spin chains from the topological AdS5×S5 stringZ. Bern : Harmony of scattering amplitudes: from N=4 super-Yang-Mills theory to

N=8 supergravityJ. de Boer : Quantum aspects of black holesR. Emparan : BlackfoldsM. Green : Supersymmetric string and eld theory scattering amplitudesS. Hartnoll : Quantum bosons for holographic superconductorsJ. Heckman : The point of E8 in F-theory GUTsS. Kachru : Gauge/gravity duality and particle physicsN. Lambert : Coupling M2-branes to background eldsJ. Louis : Compactictions and generalized geometriesM. Marino : Nonperturbative aspects of the topological stringS. Mathur : Lessons from the information paradoxL. McAllister : Ination in string theoryJ. McGreevy : Holographic descriptions of quantum liquidsJ. Polchinski : Holography from CFTA. Sen : Black hole hair removalT. Weigand : Type IIB GUT vacua and their F-theory uplift

New Trends In Quantum Integrability15th Claude Itzykson Meeting, June 2123, 2010

Organizers: D. Lebedev (ITEP Moscow), V. Pasquier, R. Santachiara (LPTMS Orsay), D. Serban.

L. Cantini : The Razumov-Stroganov correspondenceS. Derkachov : Factorization of R-matrix, Baxter Q-operators and SOVP. Dorey : The boundary staircaseL. Faddeev : Denition and use of quantum dilogarithmV. Fateev : Dierential equations for the correlation functions, elliptic conformal blocks

and AGT conjectureA. Gerasimov : A quantum eld theory model of Archimedean geometryV. Kazakov : Y-system for the exact spectrum of AdS/CFTR. Kedem : Proofs of positivity using integrable modelsG. Korchemsky : Integrability of the N=4 scattering amplitudesA. Lascoux : Deformation of Kazhdan-Lusztig and Macdonald bases

Appendices 217

S. Lukyanov : Quantum Sine(h)-Gordon model and classical integrable equationsJ.-M. Maillet : Correlation functions of quantum integrable models : the Bethe ansatz

viewpointC. Meneghelli : A shortcut to the Q operatorV. Petkova : Topological defects in Liouville CFTS. Prolhac : Fluctuations of the current in the asymmetric simple exclusion processS. Shatashvili : SUSY vacua and quantum integrabilityJ. Shiraishi : Macdonald polynomials and quantum algebrasF. Smirnov : One-point functions for sine-Gordon model at nite temperatureJ. Teschner : From modular duality to Langlands dualityA. Voros : Exact solvability of the 1D polynomial Schrödinger equation (a survey)D. Zagier : Quantum modular formsK. Zarembo : Integrability in the AdS3/CFT2 correspondence

Extremes and Records16th Claude Itzykson Meeting, June 1417, 2011

Organizers: C. Godrèche, S. N. Majumdar (LPTMS) and G. Schehr (LPTMS).

J.-M. Azais : Rice method for the extremes of gaussian random eldsE. Bertin : Renormalization group approach to the statistics of extreme values and

sumsJ.-P. Bouchaud : Correlations of extremes copula, what copula ?Z. Burda : Universal behavior of eigenvalues of the product of random gaussian ma-

trices near the edgeT. Burkhardt : Extreme value statistics of random acceleration and related processesA. Comtet : Distribution of the ground state energy in a one dimensional random po-

tentialB. Derrida : Statistics at the tip of a branching random walk and simple models of

evolution with selectionY. Fyodorov : Fluctuation properties of 1/f noise: from statistical mechanics to random

matrices, Riemann-zeta function, and Burgers turbulenceJ. Krug : Records statistics in time series with drift: theory and applicationsP. Le Doussal : Exact results for the directed polymer and KPZ growth from the Bethe

ansatzS. Nechaev : Statistics of noncoding RNAs: alignment and secondary structure predic-

tionZ. Racz : Order statistics of 1/fα signalsS. Redner : Dynamics of predatory random walkersA. Rosso : Anomalous dynamics: extremes for non-Markovian processesC. Tracy : The distributions of random matrix theory and their applicationsC. Tracy : Turbulent liquid crystals, KPZ universality, and the asymmetric simple

exclusion processM. Vrac : Statistical extreme value theory: applications in downscaling of precipita-

tionP. Yiou : Climate extreme events: an overview of physical and statistical challenges


D.15 Organization of workshops and conferences

Stéphane LavignacÉcole de Gif, (French summer school on particlephysics); since 2001.

Jean-Marc LuckRencontres de physique statistique, Paris; everyJanuary.

Stéphane NonnenmacherSpectral problems in mathematical physics,(monthly seminar at IHP), Paris; 2007.

Edmond IancuQCD, low X physics, saturation and diraction,school, Copanello, Italy; Jul 114, 2007.

Pierre VanhoveString theory and the real world: from parti-cle physics to astrophysics, summer school, LesHouches; Jul 227, 2007.

Iosif Bena37th Paris Summer Institute on Black Holes,Black Rings and Modular Forms, Paris; Aug 1324, 2007.

Edmond Iancu, Robi PeschanskiLow X meeting, Helsinki; Aug 29 Sep 1, 2007.

Bertrand Duplantier, Vincent Pas-

quier

Séminaire Poincaré, Paris; Dec 8, 2007; Jan 31,2009; Nov 21, 2009; Jun 5, 2010; Dec 4 & 18,2010.

Kirone Mallick, Robi Peschanski,Laure SauboyForum de la théorie, Saclay; Feb 78, 2008.

Cécile Monthus

Disorder and localization phenomena, from the-ory to applications, Paris; Mar 1719, 2008.

François Gélis, Edmond Iancu, Jean-Yves OllitraultHadronic collisions at the LHC and QCD at highdensity, school, Les Houches; Mar 25 Apr 4,2008.

Philippe Brax, Marco Cirelli, Géral-dine ServantProgress on old and new themes in cosmology(PONT), Avignon; Apr 21-25, 2008.

Philippe Di Francesco, Bertrand Du-

plantier

Statistical-mechanics and quantum-eld theorymethods in combinatorial enumeration, Cam-bridge, UK; Apr 2125, 2008.

Iosif BenaGravitational scattering, black holes and the in-formation paradox, workshop, Paris; May 2628,2008.

Michel Bauer, François David, Alexan-dre LefèvreOn growth and shapes, Enrage topical school,Paris; Jun 26, 2008.

Stéphane NonnenmacherMathematical aspects of quantum chaos, Mon-treal; Jun 27, 2008.

Giulio Biroli, Alexandre LefèvreManifolds in random media, random matricesand extreme value statistics, summer school,Beg Rohu; Jun 1628, 2008.

Pierre VanhoveTheory and particle physics: the LHC perspec-tive and beyond, summer school, Cargèse; Jun1628, 2008.

David Kosower, Pierre VanhoveWonders of gauge theory and supergravity, Parisand Saclay; Jun 2328, 2008.

Vincent Pasquier, Didina SerbanExact methods in low-dimensional statisticalphysics and quantum computing, Les Houches;Jun 30 Aug 1, 2008.

Olivier ParcolletFrontiers in strongly correlated systems, Aspen;Jul 27 Sep 7, 2008.

Giulio BiroliDynamical heterogeneities in glasses, colloidsand granular media, Leiden; Aug 25 Sep 5,2008.

Stéphane LavignacNNN08 Next generation nucleon decay and neu-trino detectors, Paris; Sep 1113, 2008.

Olivier ParcolletQuantum coherence and many-body correla-tions: from mesoscopic to macroscopic scales,Saclay; Oct 2223, 2008.

Marco Cirelli, Christophe GrojeanPhysics of electroweak symmetry breaking andthe LHC, workshop, Saclay; Oct 2729, 2008;Mar 23, 2009.

Stéphane NonnenmacherResonances in physics and mathematics, Mar-seille; Jan 1923, 2009.

Appendices 219

Stéphane NonnenmacherQuantum chaos, winter school, Bordeaux; Jan2630, 2009.

Jean-Paul BlaizotPhases of strongly interacting matter, school,Orsay; Mar 913, 2009.

François Gélis, Edmond Iancu, Jean-Yves OllitraultQuantum eld theory in extreme environments,Saclay; Apr 2325, 2009.

Marco CirelliTANGO in PARIS: Testing astroparticle withthe new GeV/TeV observations: positrons andelectrons, identifying the sources, Paris; May 46, 2009.

Giulio Biroli, Alexandre LefèvreQuantum physics out of equilibrium, summerschool, Beg-Rohu; Jun 1527, 2009.

Catherine PépinEmergent quantum phenomena from the nanoto the macro world, Cargèse; Jul 619, 2009.

Catherine PépinCorrelated behavior and quantum criticality inheavy fermion and related systems, Aspen; Aug9 Sep 13, 2009.

Jérémie BouttierStatistical physics, combinatorics and proba-bility: from discrete to continuous models,trimester at IHP, Paris; Sep 7 Dec 18, 2009.

Ivan Kostov, Didina SerbanFacets of integrability, Saclay and Paris; Nov 57, 2009.

Grégoire Misguich

Novel physics on the kagome network, Orsay;Jan 1820, 2010.

Vincent Pasquier, Didina SerbanPhysics in the plane: From condensed matterto string theory, Les Houches; Feb 28 Mar 5,2010.

Henri Orland, Pierre VanhoveRencontres IHÉS-IPhT, IHÉS; Mar 18, 2010.

Philippe Brax, Stéphane Lavignac,Laure SauboyGDR Terascale, Saclay; Mar 2931, 2010.

Christophe Grojean, Géraldine Ser-

vant

Planck 2010: from the Planck scale to the elec-troweak scale, CERN; May 31 Jun 4, 2010.

Francis Bernardeau, Emiliano Sefu-

satti, Filippo VernizziThe almost gaussian universe: a workshopon the observable eects of primordial non-gaussianity, Saclay; Jun 911, 2010.

Pierre VanhoveString theory: formal developments and appli-cations, summer school Cargèse; Jun 21 Jul 3,2010.

Edmond Iancu, Robi PeschanskiLow X meeting, Kavala, Greece; Jun 2327,2010.

Mariana GranaString phenomenology, Paris; Jul 59, 2010.

Francis Bernardeau, Filippo VernizziXème école de cosmologie, Cargèse; Jul 510,2010.

Marco Cirelli, Gabrijela ZaharijasTeV particle astrophysics, Paris; Jul 1923,2010.

Henri Orland, Philippe Di FrancescoStatphys24, Cairns, Australia; Jul 1923, 2010.

Christophe Grojean, Géraldine Ser-

vant

Physics at TeV colliders - from Tevatron to LHC,Cargèse; Jul 1931, 2010.

Marco CirelliICHEP International conference on high en-ergy physics, Paris; Jul 2228, 2010.

Iosif BenaICHEP Track 12 Beyond quantum eld theoryapproaches (including string theories), Paris; Jul2228, 2010.

Giulio Biroli, Alexandre LefèvreConcepts and methods of statistical mechanics,summer school, Beg Rohu; Aug 23 Sep 4, 2010.

Marco CirelliCosmic rays for particle and astroparticlephysics (ICATPP), Como, Italy; Oct 78, 2010.

Marco CirelliECFA study of physics and detectors for a linearcollider, Geneva; Oct, 2010.

Enrico Goi, Francesco OrsiStrings, cosmology and gravity student confer-ence (SCGSC), Paris; Nov 35, 2010.

Marco CirelliDark matter all around, Paris; Dec 13-17, 2010.

Edmond IancuExcited QCD 2011, Les Houches; Feb 2025,2011.


Philippe Brax, Chiara Caprini, MarcoCirelli, Géraldine ServantProgress on old and new themes in cosmology(PONT), Avignon; Apr 1822, 2011.

Stéphane NonnenmacherSpectral gap in dynamical systems, number the-ory and PDEs, Peyresq, France; May 30 Jun3, 2011.

Appendices 221

D.16 Research administration

Who Assignment Institution

A. Billoire

Coordinator of call projects inmathematics, physics, andcommunication technologies(2007 2011)

Région Rhône-Alpes

F. BernardeauChairman of the AERESevaluation committee (2009)

LUTH

Scientic committee (CSTS) Irfu/SAPScientic committee (since2008)

Cargèse School

F. DavidComité de programmationscientique (until end 2009)

Institut Henri Poincaré, Paris

Peer review evaluation panel,Starting grants (since 2007)

European Research Council (ERC)

AERES evaluation committee(2008)

Institut Jean Lamour and the labora-tories UMR 7040, 7555, 7556, 7570 &7584 (Nancy)


Fédération Dynamique des SystèmesComplexes (UPMC, Paris)


Institut Non-Linéaire de Nice (INLN)and the Federation Wolfgang Döblin(CNRS - Univ. Nice Sophia Antipolis)

In charge of the Intergroupedes théoriciens

French Physical Society

B. Duplantier Scientic committee IHÉS

Selection committeeUniv. Diderot-Paris 7, Univ. Versailles-Saint Quentin

O. GolinelliComité d'évaluation(20092011)

GENCI Grand équipement nationalde calcul intensif

C. GrojeanScientic committee(20072009)

Service de Physique des Particules,CEA Saclay (IRFU/SPP)

International Detector AdvisoryGroup (20082012)

International Linear Collider

Commission consultative despécialistes (20102014)

Univ. Paris XI

S. LavignacSelection committee(20072008, 2011)

Université Pierre et Marie Curie - Paris6

J.-M. LuckBureau de l'axe B & Comité dela vie scientique

RTRA Triangle de la physique.

Elected member (up to 2008)Section 02 of the national committee ofCNRS.

Commission consultative despécialistes (20102014)

Sections 29 & 34, Univ. Paris XI (Or-say)

S. Nonnenmacher Selection committee (2009) ENS Paris

J.-M. Normand

Work package FuturePetaop/s computertechnologies beyond 2010(co-leader), Work packagePetaop/s systems for2009/2010 (20082010)

Partnership for advanced computing inEurope (PRACE), Preparatory phase

Work package Futuretechnologies (20102011)

PRACE, 1st implementation phase

J.-Y. Ollitrault Board of directors (since 2009) ECT* Trento


H. Orland Vice-presidentIUPAP (International Union of Pureand Applied Physics)

ChairStatistical physics Commission (C3) ofthe IUPAP

O. ParcolletComité thématique CT5(20092011)

GENCI Grand équipement nationalde calcul intensif

G. ServantScientic committee (since2008)

Institut d'Etudes Scientiques deCargèse

P. Vanhove Founding member (2009)Institute for Physics and Mathematicsof the Universe

LHC safety commitee for theAutorité de Sûreté Nucléaire(2008)

LHC

Elected member (2008 2012)CNRS national committee, section 02(Théories physiques: méthodes, mod-éles et applications)

Coordinator of the IPhTsub-node for the EuropeanNetwork Forces Universes (2005 2009)

Europe

Appendices 223

D.17 IPhT and high performance computing

CEA computers

CEA has shared supercomputer resources, whichare among the largest in France and even Eu-rope. They are managed by the CCRT (Cen-tre de Calcul Recherche et Technologie, Re-search and Technology Computing Centre). ThePhysics Division of CEA, DSM, contributesabout 25% to CCRT. Scientic projects requir-ing large computer resources are submitted toa scientic committee, which distributes com-puter time. Since created in 1994, the head ofthis committee is the head of our Institute. Thesecretary of the committee is also a physicist ofour Institute, Olivier Golinelli.

National computers

Several members of the IPhT are involved inthe scientic evaluation of applications for com-puting time at the GENCI (Grand ÉquipementNational de Calcul Intensif, the organizationthat manages the main computer centers of theFrench public research): Olivier Parcollet is amember of the Thematic Committee CT5, "The-oretical physics and plasma physics"; OlivierGolinelli represents the CEA in the EvaluationCommittee.

European computers

Building a world-class pan-European High Per-formance Computing (HPC) Service was a chal-lenge involving governments, funding agencies,centres capable to host and manage the su-percomputers, and the scientic and industrialuser communities with leading edge applica-tions. This has to be done in a quickly evolvingcontext. An HPC Infrastructure has two uniquecharacteristics: supercomputers serve all scien-tic disciplines and leading edge supercomput-ers (Tier-0 systems) have a three year depreci-ation cycle. This requires a periodic renewal ofthe systems and a continuous upgrade of the in-frastructure. Furthermore, technologies changecontinuously, novel architectures and systemdesigns will be created and the science focuschanges as results are obtained and new direc-tions are explored.

The Partnership for Advanced Computingin Europe Research Infrastructure (PRACE RI,www.prace-ri.eu) has been founded in April 2010with its seat in Brussels. Four nations (France,Germany, Italy and Spain) have agreed to pro-vide 400 million Euro to implement Tier-0 sys-tems with a combined computing power in themulti Petaop/s (one quadrillion operations per

second) range over the next 5 years. This fund-ing is complemented by up to 70 million Eu-ros from the European Commission (EC) whichis supporting the Preparation and Implementa-tion of this infrastructure. Presently, PRACEhas two Tier-0 systems: the 1 Petaop/s IBMBlueGene/P (JUGENE) of the Gauss Centre forSupercomputing (GSC) hosted by FZJ, Jülich,Germany and the 1.6 Petaop/s Bull Bullx clus-ter (CURIE), funded by GENCI and installed atCEA CCRT, Bruyères-le-Châtel, France, whichwill reach its full performance in the secondhalf of 2011. In the third quarter of 2011,the GCS partner HPC Center of UniversityStuttgart will deploy the rst installation step ofa 1 Petaop/s Cray system (Hermit), followedby a 4-5 Petaop/s second step in 2013. Thefourth system Tier-0 system, a 3 Petaop/s IBM(SuperMUC), will be available in mid 2012 atthe GCS partner LRZ-Garching, Munich, Ger-many. The Spanish and the Italian systems areplanned for later (respectively at BSC Barcelonaand CINECA Bologna). To keep pace withthe needs of the user communities and techni-cal developments, systems within the PRACERI are expected to reach capabilities of at leastone Exaops/s (one quintillion) in less than adecade. Access for European researchers andtheir collaborators is determined based on pro-posals submitted in response to Calls for Pro-posals (www.prace-ri.eu/hpc-access). These areissued twice a year and are evaluated by lead-ing scientists and engineers in a peer-review pro-cess governed by a PRACE Scientic SteeringCommittee. Users will be supported by expertsin porting, scaling, and optimizing applicationsto novel, highly parallel computer architectures.An in-depth training program accompanies thePRACE oering teaching scientists and studentshow to best exploit the unprecedented capabili-ties of the systems. PRACE RI has presently 21European members. Within PRACE activities,France is represented by GENCI with its threemain components, CEA (CCRT at Bruyères-le-Châtel), CNRS (IDRIS at Orsay) and the Uni-versity (CINES at Montpellier), in addition, IN-RIA recently join.

Jean-Marie Normand has been deeply in-volved in the PRACE Preparatory Phase pe-riod (January 2008 until June 2010), especiallyin two among the eight Work packages (WP):in WP7 Petaop/s systems for 2009/2010, forrecommendations about the rst systems to bedeployed and in WP8 Future Petaop/s com-


puter technologies beyond 2010. At the requestof Prof. Dr. Dr. Thomas Lippert, Head ofJülich Supercomputing Centre and Director ofInstitute for Advanced Simulation, J.-M. Nor-mand led the WP8, dening and setting up thecollaborative work, organizing several Technol-ogy survey meetings and completing success-fully a selection process of prototypes funded bythe EC. Within the PRACE 1st Implementa-tion Phase (www.prace-project.eu) Period (July2010 up to now), J.-M. Normand actively con-tributes to WP9 Future Technologies (nowled by Herbert Hubert, LRZ Garching, Ger-many). The objectives are (i) the assessmentof emerging hardware and software technolo-gies for multi-Petascale systems, (ii) the evalua-tion of future programming paradigms and (iii)the evaluation of energy ecient HPC solutions.Since 2008, J.-M. Normand contributes withinGENCI to the coordination of PRACE activi-ties at the French level, strengthening the col-laboration among the three components CCRT,IDRIS and CINES. A PRACE Second Imple-mentation Phase 2 year project, PRACE-2IP,will be launched on September 1st, 2011, ded-icated mainly to the integration of the alreadyexisting organization DEISA with PRACE RI.

Since December 2010, Jean-Marie Normand

is appointed as CEA's International Expertin the eld Mathematics, Informatics, Softwareand Systems Technologies with speciality Sys-tem and Network.

Focusing his activity on energy eciency, en-ergy consumption and high computing density,J.-M. Normand sent a long document to theCEA Direction (General Administrator, HighCommissioner, Strategy and Programme Direc-tor) in January 2011. Coping with a contin-uously increasing demand of strategic comput-ing power, this document underlines that thesemain issues are a unique opportunity for Europeto become an actor in the design and construc-tion of high performance energy ecient (green)computing systems. Indeed, the CEA, withmainly DRT-LETI and LIST, DAM-DSSI andDSM-INAC-SPINTEC, the Europe with severalstrong industrial positions in HPC and above allin embedded computing, have many assets tocarry on such an ambitious challenge. A CEAprogramme meeting of the Strategic OrientationCommittee (COMOS) took place in April 2011on these topics with the main presentation givenby J.-M. Normand. Discussions continue, espe-cially with the High Commissioner Cabinet, theStrategy and Programme Direction and mainlythe DRT-LETI and LIST.

Appendices 225

D.18 Scientic editing

Who Role JournalI. Bena Advisory panel Journal of Physics A

F. Bernardeau Editorial BoardReport on Progress in Physics journal (IOP publica-tions)

F. Bernardeau,C. Grojean

Co-editorParticle physics and cosmology: the fabric of space-time, Proceedings of the LXXXVI Les Houches Sum-mer School (2007).

G. Biroli,P. Di Francesco,B. Eynard,C. Godrèche,D. Serban

EditorsJSTAT (Journal of statistical mechanics: theory andexperiment)

B. Duplantier Editor Nuclear Physics B [FS]Editor Journal of Statistical PhysicsEditor La gazette des mathématiciens (SMF)ExecutiveCommittee

Annales Henri Poincaré

Editor-in-ChiefPoincaré Seminar Series in Progress in MathematicalPhysics, Birkhäuser Science [t08/239, t10/222, t10/224]

C. Grojean Co-editorNew physics at the LHC: a Les Houches report. Physicsat TeV Colliders 2007, New physics working group; LesHouches [t08/276]

Co-editorNew Physics at the LHC: a Les Houches report: Physicsat TeV Colliders 2009; Les Houches [t10/305]

Co-editorFrom the LHC to future colliders, Eur. Phys. JournalC66 525583, [t09/294]

R. Guida Editor ScholarpediaJ.-M. Luck Editorial Board Journal of Statistical Physics

Advisory Panel Journal of Physics AS. Nonnenmacher co-editor Nonlinearity (2004-2012)

co-editor European Physical Journal B (2007-2010)H. Orland Editor Physics Reports (Elsevier)V. Pasquier,D. Serban

Co-editorsLes Houches Summer School Proceedings, July 2008,[t08/289]

P. Vanhove Co-editorTheory and Particle Physics: the LHC perspective andbeyond [Nucl. Phys. B Proc. Suppl. 192-193 (2009)]

Co-editorString Theory and the real World: From ParticlePhysics to Astrophysics - Les Houches Summer SchoolProceedings Volume 87, 2008

Co-editorStrings and Branes: The present paradigm for gauge in-teractions and cosmology [Nucl. Phys. B Proc. Suppl.171 (2007)]







http://www.scholarpedia.org



D.19 Internal organization

D.19.1 Aliation, direction

The IPhT (Institut de physique théorique)named SPhT (Service de physique théorique un-til mid 2007) is an institute of DSM (Directiondes sciences de la matière), the Physics divisionof CEA (Commissariat à l'énergie atomique).IPhT is also aliated with the national researchcenter, CNRS, under the reference URA 2306.

The Head of the institute was Henri Orlandfrom 2004 to 2010, and Michel Bauer since Jan-uary 2011. The head is assisted by two deputies,Anne Capdepon, and Olivier Golinelli (who re-placed Jean-Yves Ollitrault in 2009)

The institute is informally divided into threegroups:Models and structures: mathematical physics,Cosmology and particle physics,Statistical physics and condensed matter phy-sics.

D.19.2 Committees

Evaluation

Our activity is reviewed on a regular basis by anevaluation committee (Conseil scientique ex-térieur). The present report is meant to serve asa written basis for the evaluation of the periodextending from June 2007 to May 2011. Thevisit of the Institute by the committee is planedon Nov 2122, 2011. The members are:

Leon Balents (KITP, Santa Barbara, USA),Edmund Bertschinger (MIT, Cambridge, USA),Alain Comtet (LPTMS, Université Paris-Sud,France), Vladimir Fateev (LPTA,UniversitéMontpellier II, France), Jean-François Joanny(Institut Curie, Paris, France), Dieter Lüst(Ludwig-Maximilians Universität, München,Germany), Giuseppe Marchesini (Dipartimentodi Fisica, Università Milano-Bicocca, Italy),David Mukamel (Department of Physics of Com-plex Systems, Weizmann Institute of Science, Is-rael) Graham Ross (Department of Physics, Uni-versity of Oxford, UK), George Sterman (C.N.Yang Institute for Theoretical Physics, StonyBrook, USA), Martin Zirnbauer (Institut fürTheoretische Physik, Universität zu Köln, Ger-many).

Local scientic committee (Conseil scien-tique)

A local scientic committee is elected every sec-ond year among the permanent physicists of theinstitute. It assists the Head of the institutewith scientic decisions, in particular hirings.

The minutes of meetings can be downloadedfrom the intranet webpage.

Apart from the head and his deputies, themembers were:

in 2007, Michel Bauer, Giulio Biroli (secre-tary), Philippe Brax, Bertrand Eynard, EdmondIancu, Hubert Saleur;

in 20082009, Alain Billoire , David Kosower,Stéphane Lavignac, Stéphane Nonnenmacher(secretary), Vincent Pasquier;

in 20102011, François Gélis, Stéphane Lav-ignac (secretary), Ruben Minasian, Henri Or-land, Olivier Parcollet, Didina Serban.

Institute committee (Conseil de laboratoire)

The Institute committee is in charge of prac-tical matters. It aims at facilitating everydaylife. It consists in average of eight members,who are elected for two years: three permanentphysicists, two administrative sta, one emeritusphysicist, one PhD student, and one postdoc. Itnormally meets three times per year. The min-utes of meetings can be downloaded from theintranet webpage.

Apart from the head and his deputies, themembers were:

in 2007, François David, Bertrand Du-plantier, Michele Frigerio, André Morel, NicolasOrantin, Olivier Parcollet, Laure Sauboy (secre-tary);

in 20082009, Iosif Bena, Patrick Berthelot,Jérémie Bouttier, Catherine Cataldi, MicheleFrigerio, Riccardo Guida, Clément Ruef (secre-tary), Alexandre Thaumoux;

in 20102011, Iosif Bena, Camille Bonvinreplaced by Javier Lopez-Albacete and Jose-Miguel No, Jérémie Bouttier, Chiara Caprini,Émeline Cluzel, Laurent Sengmanivanh (secre-tary), Alexandre Thaumoux.

D.19.3 Support

Administrative secretaries

The Institute has three secretaries, for a totalof roughly 100 people (short term visitors arenot included in this estimate). The name secre-taries is historical but misleading, and is usedonly as a shortcut for the endless list of little andbig things they do for the welfare of the Insti-tute. Nowadays, the name assistants would bemore appropriate. They are multitalented, withsharp skills.

Sylvie Zaanella is the Secretary of the Headof the Institute. She is also in charge of hu-man resources management, equipment pur-

Appendices 227

chase, and travel (to conferences, etc.). Most ofour accounting is managed by a dierent insti-tute, the IRAMIS, for historical reasons. How-ever, CNRS money is managed locally by Sylvie.using a dedicated software, XLAB.

Catherine Cataldi is in charge of PhD stu-dents, postdocs, and long-term (> 1 month) vis-itors.

Laure Sauboy has the responsibility of short-term visitors, whose number is continuously in-creasing. She also keeps track of fundings andgrants (Marie-Curie, ANR, etc.).

The secretaries also help for the organizationof conferences and meetings.

As a byproduct of the expansion of theIPhT, due mainly to non-permanent members,the workload of the secretaries has reached (orcrossed) the limits of what is acceptable, withconsequences for them, but also for our visitors.

Library and electronic resources

Our local library owns as many as 11000 books.It is shared with the neighbouring CondensedMatter Physics Department (SPEC). It has un-dergone a profound mutation due to the spreadof electronic publishing. In 2007 we still receivedpaper versions of 120 journals, but in 2011 thisnumber has dropped by one order of magnitudeor almost. This mutation will continue duringthe next few years.

The support of the library is now providedsolely by Bruno Savelli. He is in charge of main-taining the library, and of repair works. Wetry however to maintain the quality of our bookfund: the library is still an important work-ing tool for the researchers. The choice of ac-quisitions is carried out by the physicists whoselect the new books, decide how to organizethe themes and which of the stolen/lost booksshould be bought again. This process is coordi-nated by Riccardo Guida.

We maintain a local repository of our publi-cations, which is fed by physicists since Novem-

ber 2007, when our library manager, Marc Gin-gold, retired.

The computer team

The management of the computer system isshared with the IRAMIS (Institut RayonnementMatière de Saclay). The group is composed of 8people, under the direction of Jean-Louis Greco(IRAMIS).

The local team at Orme des Merisiers, whichis mostly in charge of Unix and Linux ma-chines, is composed of 4 people: Pascale Beurtey(IRAMIS) is in charge of the team. She joinedthe group in 2007, and replaced Anne Capde-pon. Philippe Caresmel (IRAMIS) was hiredin July 2007 to replace Olivier Croquin, wholeft in March. Similarly, Laurent Sengmanivanh(IPhT) was be hired in November 2007 to re-place Christian Perez, who left in April. Finally,Patrick Berthelot (IPhT) is in charge of main-taining local Windows machines and the wirelessnetwork.

A committee composed of physicists (cur-rently: Jérémie Bouttier, Anne Capdepon,François David, François Gélis, Jérôme Hou-dayer, Grégoire Misguich (secretary) and LenkaZdeborova) and the local computer team de-cides the future orientations of our computersystem, makes purchase decisions and informsthe physicists about changes. The minutes ofthis committee can be downloaded from our in-tranet webpage.

Miscellanea

Loïc Bervas, who was until 2007 our scienticsecretary, now cumulates a number of scatteredbut important functions. To list only the mainones, he takes care of orders and inventories(standard furnitures, computers, consumablesand so on) of the IPhT; he also helps extract-ing from the main CEA databases (and puttingin human readable form) the incomes and ex-penses of the IPhT, especially those related toexternal fundings.


D.20 Permanent members of IPhT

Support

Patrick BerthelotLoïc BervasAnne CapdeponCatherine CataldiLaure Sauboy

Bruno SavelliLaurent Sengmanivanh (since 2007)Alexandre Thaumoux (2008 2011)Sylvie Zaffanella

Physicists, CEA

Marc Barthélemy (since 2009)Michel BauerIosif BenaFrancis BernardeauAlain BilloireGiulio BiroliJérémie BouttierPhilippe BraxRuth Britto (since 2008)Philippe Di FrancescoBertrand DuplantierBertrand EynardFrançois GelisClaude GodrècheOlivier GolinelliMariana GrañaChristophe Grojean (at CERN since 2006)Riccardo GuidaEmmanuel Guitter

David KosowerJean-Marc LuckKirone Mallick

Grégoire Misguich

Stéphane NonnenmacherJean-Marie NormandHenri OrlandOlivier ParcolletVincent PasquierCatherine PépinHubert SaleurDidina SerbanGéraldine Servant (at CERN since 2006)Jean-Louis SikoravPatrick ValageasPierre VanhoveFilippo Vernizzi (since 2008)André Voros (until 2008)

Physicists, CNRS

Michel Bergère (until 2010)Jean-Paul BlaizotChiara Caprini (since 2008)Marco Cirelli (since 2007, at CERN since2009)François DavidThomas GarelJérôme HoudayerEdmond IancuGregory Korchemsky (since 2008)

Ivan KostovStéphane LavignacAlexandre Lefèvre (until 2010)Ruben Minasian

Cécile Monthus

Christiane NormandJean-Yves OllitraultCarlos Savoy (until 2008)Gregory Soyez (since 2010)Lenka Zdeborova (since 2010)

Conseillers scientiques CEA, Emerita CNRS and Association Pour la science

Roger BalianMichel Bergère (since 2010)Jacques BrosMarc Chemtob (since 2007)Henri Cornille (until 2008)Cirano De DominicisBertrand GiraudAndré Morel

Pierre Moussa

Robi PeschanskiMannque RhoGeorges RipkaCarlos Savoy (since 2008)Richard SchaefferEdgar SouliéAndré Voros (since 2008)Jean Zinn-Justin

Documents

IPhT Institut de Physique Théorique de Saclay Rapport d'activité juin