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Phenomenological Aspects of Local String Models
F. Quevedo, Cambridge/ICTP. PASCOS-2011, Cambridge.
M. Dolan, S. Krippendorf, FQ; arXiv:1106.6039 S. Krippendorf, M. Dolan, A. Maharana, FQ; arXiv:1002.1790 C. Burgess, A. Maharana, FQ; arXiv:1005.1199 C. Burgess, M. Cicoli, M. Gomez-Reino, FQ, G. Tasinato, I. Zavala; arXiv1005.4840
String Phenomenologists:
Strategic (long term) Plan: String theory scenario that satisfies
all particle physics and cosmological observations and
hopefully lead to measurable predictions
String Phenomenology
• Too many string models? (Heterotic, IIA, I, IIB, Landscape,...)
• Or too ‘few’ models? (Realistic?)
Recall LHC is running: Hierarchy Problem Proposals
• TeV SUSY
• Warped extra dimensions
• Large extra dimensions
• … UV complete? How to fix size of extra dimensions? Unification, Flavour, Proton stability,…
Challenges for String Models • Gauge and matter structure of SM • Hierarchy of masses (including neutrinos) • Flavor CKM, PMNS mixing, CP no FCNC • Hierarchy of gauge couplings (unification?) • ‘Stable’ proton + baryogenesis • Dark matter (+ avoid overclosing) • Inflation or alternative for CMB fluctuations • Dark energy
N.B. If ONE of them does not work, rule out the model!!!
Bottom-up Approach
• Gauge group • Chiral spectrum • Yukawa couplings • Gauge couplings • Proton stability • Flavour symmetries
• Moduli Stabilisation • Cosmological constant • SUSY Breaking • Scales (unification,
axions,…) • Inflation, Reheating • Cosmological moduli
problem
Local (brane) Properties Global (bulk) Properties
MODULI STABILISATION
4-cycle size: τ (Kahler moduli)
3-cycle size: U (Complex structure moduli)
+ String Dilaton: S
Exponentially Large Volumes Example :
Exponentially large volumen + Broken SUSY!!!
Fluxes
Volume
Perturbative (alpha’) corrections to K
Nonperturbative corrections to W
e.g.: Anisotropic Moduli Fixing • K3 Fibrations:
Poly-Instantons
K3 ! size t22
i=3, j=1
Blumenhagen et al.
Relevant Scales • String scale Ms=MP/V 1/2
• Kaluza-Klein scale MKK=MP/V 2/3
• Gravitino mass m3/2=W0 MP/V
• Volume modulus mass MV=Mp/V 3/2
• Lighter (fibre) moduli Ml=Mp/V 5/3
General Scenarios • MString = MGUT~ 1016 GeV (V~105)
• W0~10-11<<1 (or W0~1 plus warping) to get TeV soft terms • Fits with coupling unification • Natural scale of most string inflation models. • Axi-volume quintessence scale (w=-0.999….)
• MString = Mint.~ 1012 GeV (V~1015)
• W0~1 • m3/2~1 TeV (solves hierarchy problem!!!) • QCD axion scale • neutrino masses LLHH
• MString = 1 TeV (V~1030) • W0~1 • Most exciting, 5th Force OK m~10-3 eV, if SM non SUSY. Back reaction?
Kähler Moduli Inflation (Blow-up)
volume τn
V Small field inflation (r<<<1) No fine-tuning!! 0.960<n<0.967 Loop corrections??
~
Ne
ns
ns
r r
Observable gravity waves !
(can be ruled out by Planck if they observe them and CMBpol… if they do not observe them)
LARGE Volume Implies Standard Model is localised ! ( SM D7 cannot wrap the exponentially large cycle since g2=1/V2/3 ) ‘Bottom-up’ (AIQU 2000) Fractional D3/D7 Brane at a singularity (collapsed cycle)
Magnetised D7 - Brane wrapping a ‘small’ four-cycle
Local F-Theory Blumenhagen et al.
Donagi, Wijnholt; Vafa, Heckman, …
Aldazabal et al.
D3 Branes at Singularities
• Orbifolds • Del Pezzos 0-8
(dPn=P2 blown-up at n arbitrary points c1>0, b2=n+1, 2n-8 parameters, n>3)
• Larger class: Toric singularities (infinite class of models!!!)
Toric Singularities
Einstein-Sasaki
T3 Fibration Over rational polyhedral cone
Toric Diagram
D3-branes
Del Pezzo Singularities/Quivers e.g. del Pezzo 0 (C3/Z3)
ni D3 Branes (group ПU(ni))
mj D7 Branes (group ПU(mi))
Arrows=bi-fundamentals
Anomaly/tadpole cancelation
Hypercharge (ni≠nj)
3 Families!
D7s:Franco-Uranga
General Results Toric 1. Maximum number of families = 3 (except for one case F0 with 4 families,
dual to a 2-family model, also non-toric phases unbounded)
2. Quark Mass hierarchy: (M,m,0) with M>>m
(structure of Yukawas imply one zero e-value, only dP0 has m=M)
Generic Features
• Aproximate Flavour Symmetries
• Hyperweak Interactions (SM fields charged under D7 gauge interactions g2=1/V2/3 <<<1, CDF?)
Burgess et al. 2008
Conlon, Maharana, FQ
The Needle on a Haystack (search with a magnet!)
• Not simple GUT groups (SU(5), SO(10),…) Search for PS, LR, SM,…
• Many U(1)’s but if U(1)Y= Σi U(1)i, ‘wrong’ normalisation for MSSM unification (5/3). Also keep hypercharge massless in compact case.
• Then U(1)Y in G non-abelian (SU(4),…)
• ALL SM in D3’s at least G=PS, SU(3)3
Minimal del Pezzo?
• dP0 no hierarchy of masses (unless non-commutative), no CKM
• dP1, dP2 no CKM or PMNS, no control of kinetic terms (FCNC?).
• dP3 flavor diagonal kinetic terms and realistic CKM, PMNS matrices.
‘Realistic’ ‘Pati-Salam’ Model (dP3)
• Break symmetry to SM (+ U(1) or LR) • Breaking U(1) to SM: RH sneutrino
(R-parity broken) • Quark+ lepton mass hierarchies • See-saw neutrino masses • Stable proton • CKM, CP • Controlled kinetic terms!! !!! • Gauge Unification
Gauge Coupling Unification
String scale value of all couplings given by dilaton so unification.
Standard GUT scale unification or ‘intermediate’ scale Ms>1012 GeV
Need moduli stabilisation to fix scales.. (Large volume scenarios?....)
SUSY Breaking • Approximate Universality
• Two cases: FSM≠0 soft terms~m3/2 Ms~10
12 GeV
FSM=0 soft terms <<m3/2
or~m3/2
CAQS, Conlon (Mirror Mediation)
CONCLUSIONS • Continuous progress on local string
models (TeV warping, TeV gravity, TeV SUSY!?)
• Several SUSY breaking scenarios (m~m3/2, m3/2
3/2/Mp1/2, m3/2
2/Mp ), (Ms~103 – 1016 GeV) • Local model building (dP3: 3-families, mass
hierarchies (M,m,0), CKM, PMNS, Unification, proton stable,…) • Concrete models of inflation (gravity waves
and non-gaussianities) • Many open questions