1 The chiral magnetic effect: from quark-gluon plasma to Dirac semimetals D. Kharzeev High Energy Physics in the LHC Era, Valparaiso, Chile, 2012 “Quarks

1 The chiral magnetic effect: from quark-gluon plasma to Dirac semimetals D. Kharzeev High Energy Physics in the LHC Era, Valparaiso, Chile, 2012 Quarks 2014, Suzdal, Russia, 2-8 June, 2014

What is Chiral Magnetic Effect? 2 Chirality imbalance + Magnetic field = Electric current Talks at Quarks 2014: V. Braguta, T. Kalaydzhyan, A. Kotov

Quantum anomalies 3 Anomalies: The classical symmetry of the Lagrangian is broken by quantum effects - examples: chiral symmetry - axial anomaly scale symmetry - scale anomaly Anomalies imply correlations between currents: e.g. decay A V V if A, V are background fields, V is not conserved!

Quantum anomalies 4 A In classical background fields (E and B), chiral anomaly induces a collective motion in the Dirac sea

Chiral Magnetic Effect in a chirally imbalanced plasma Fukushima, DK, Warringa, PRD08 In the presence of the chiral chemical potential and in magnetic field, the vector e.m. current is not conserved: Compute the current through The result: Coefficient is fixed by the axial anomaly, no corrections 5

Some of the earlier work on P-odd currents 6 Vilenkin 78 Eliashberg 83 Rubakov, Tavkhelidze, 85 Levitov, Nazarov, Eliashberg 85 Wilczek 87 Alekseev, Cheianov, Frohlich 98 Joyce, Shaposhnikov 97 Review: DK, Prog. Part. Nucl. Phys. 2014

Chiral magnetic conductivity: discrete symmetries 7 P-even T-odd P-odd T-odd P-odd effect! T- even Non-dissipative current! (quantum computing etc) cf Ohmic conductivity: P-even, T-odd, dissipative

Systematics of anomalous conductivities 8 Vector current Axial current Magnetic fieldVorticity

46 Heavy ion collisions as a source of the strongest magnetic fields available in the Laboratory DK, McLerran, Warringa, Nucl Phys A803(2008)227

47 Heavy ion collisions: the strongest magnetic field ever achieved in the laboratory

46 Magnetic fields in heavy ion collisions In a conducting plasma, Faraday induction can make the field long-lived K.Tuchin, arXiv:1006.3051, 1305.5806 U.Gursoy, DK, K. Rajagopal, arXiv:1401.3805 L.McLerran,V.Skokov arXiv:1305.0774

46 Magnetic fields in heavy ion collisions U.Gursoy, DK, K. Rajagopal, arXiv:1401.3805 Observable effects on directed flow of charged hadrons: Faraday Faraday + Hall

Numerical evidence for chiral magnetic effect in lattice gauge theory, P. Buividovich, M. Chernodub, E. Luschevskaya, M. Polikarpov, ArXiv 0907.0494; PRD SU(2) quenched, Q = 3; Electric charge density (H) - Electric charge density (H=0) Red - positive charge Blue - negative charge

Chiral magnetic effect in 2+1 flavor QCD+QED, M. Abramczyk, T. Blum, G. Petropoulos, R. Zhou, ArXiv 0911.1348; 2+1 flavor Domain Wall Fermions, fixed topological sectors, 16^3 x 8 lattice Red - positive charge Blue - negative charge

Electric dipole moment of QCD instanton in an external magnetic field 15 G. Basar, G. Dunne, DK, arXiv:1112.0532 [hep-th] Topological charge density Quark zero mode density Asymmetry between left and right modes induces the e.d.m. in an external B B=0 B>0

16 Arxiv:1401.4141

17 No sign problem for the chiral chemical potential - direct lattice studies are possible Fukushima, DK, Warringa, PRD08

18 arXiv:1105.0385, PRL + Talks by V. Braguta and A. Kotov

The Chern-Simons diffusion rate in an external magnetic field 19 G. Basar, DK, Phys Rev D, arXiv:1202.2161 strongly coupled N=4 SYM plasma in an external U(1) R magnetic field through holography weak field: strong field increases the rate: dimensional reduction

Holographic chiral magnetic effect: the strong coupling regime (AdS/CFT) H.-U. Yee, arXiv:0908.4189, JHEP 0911:085, 2009; V. Rubakov, arXiv:1005.1888,... A. Rebhan, A.Schmitt, S.Stricker JHEP 0905, 084 (2009), G.Lifshytz, M.Lippert, arXiv:0904.4772;.A. Gorsky, P. Kopnin, A. Zayakin, arXiv:1003.2293, T. Kalaydzhyan, I. Kirsch 11,.. CME persists at strong coupling - hydrodynamical formulation? D.K., H. Warringa Phys Rev D80 (2009) 034028 Strong coupling Weak coupling

Hydrodynamics and anomalies Hydrodynamics: an effective low-energy TOE. States that the response of the fluid to slowly varying perturbations is completely determined by conservation laws (energy, momentum, charge,...) Conservation laws are a consequence of symmetries of the underlying theory What happens to hydrodynamics when these symmetries are broken by quantum effects (anomalies of QCD and QED)? 21

Chiral MagnetoHydroDynamics (CMHD) - relativistic hydrodynamics with triangle anomalies and external electromagnetic fields 22 First order (in the derivative expansion) formulation: D. Son and P. Surowka, arXiv:0906.5044 Constraining the new anomalous transport coefficients: positivity of the entropy production rate, CME (for chirally imbalanced matter)

Chiral MagnetoHydroDynamics (CMHD) - relativistic hydrodynamics with triangle anomalies and external electromagnetic fields 23 First order hydrodynamics has problems with causality and is numerically unstable, so second order formulation is necessary; Complete second order formulation of CMHD with anomaly: DK and H.-U. Yee, 1105.6360; Phys Rev D Many new transport coefficients - use conformal/Weyl invariance; still 18 independent transport coefficients related to the anomaly. 15 that are specific to 2nd order: new Many new anomaly-induced phenomena!

Chiral MagnetoHydroDynamics (CMHD) - relativistic hydrodynamics with triangle anomalies and external electromagnetic fields 24 DK and H.-U. Yee, 1105.6360 Positivity of entropy production - still too many unconstrained transport coefficients... Is there another guiding principle?

No entropy production from T-even anomalous terms 25 P-even T-odd P-odd T-odd P-odd effect! T- even Non-dissipative current! (time-reversible - no arrow of time, no entropy production) cf Ohmic conductivity: T-odd, dissipative DK and H.-U. Yee, 1105.6360

No entropy production from P-odd anomalous terms 26 DK and H.-U. Yee, 1105.6360 Mirror reflection: entropy decreases ? Decrease is ruled out by 2nd law of thermodynamics Entropy grows

No entropy production from T-even anomalous terms 27 1st order hydro: Son-Surowka results are reproduced 2nd order hydro: 13 out of 18 transport coefficients are computed; but is the guiding principle correct? Can we check the resulting relations between the transport coefficients? e.g. DK and H.-U. Yee, 1105.6360

The fluid/gravity correspondence 28 DK and H.-U. Yee, 1105.6360 Long history: Hawking, Bekenstein, Unruh; Damour 78; Thorne, Price, MacDonald 86 (membrane paradigm) Recent developments motivated by AdS/CFT: Policastro, Kovtun, Son, Starinets 01 (quantum bound) Bhattacharya, Hubeny, Minwalla, Rangamani 08 (fluid/gravity correspondence) Some of the transport coefficients of 2nd order hydro computed; enough to check some of our relations, e.g. J. Erdmenger et al, 0809.2488; N. Banerjee et al, 0809.2596 It works Other holographic checks work as well:

The chiral magnetic current is non-dissipative: protected from (local) scattering and dissipation by (global) topology Somewhat similar to superconductivity, but can exist at high temperature! Anomalous transport coefficients in hydrodynamics describe dissipation- free processes (unlike e.g. shear viscosity) 29

DK, H.-U. Yee, arXiv:1012.6026 [hep-th]; PRD The CME in relativistic hydrodynamics: The Chiral Magnetic Wave 30 Propagating chiral wave: (if chiral symmetry is restored) Gapless collective mode is the carrier of CME current in MHD: CME Chiral separation Electri c Chiral

The Chiral Magnetic Wave 31 DK, H.-U. Yee, arXiv:1012.6026 [hep-th], PRD The velocity of CMW computed in Sakai- Sugimoto model (holographic QCD) In strong magnetic field, CMW propagates with the speed of light! Chiral Electri c

32 Testing the Chiral Magnetic Wave Y.Burnier, DK, J.Liao, H.Yee, PRL 2011 Finite baryon density + CMW = electric quadrupole moment of QGP. Signature - difference of elliptic flows of positive and negative pions determined by total charge asymmetry of the event A: at A>0, v 2 (-) > v 2 (+); at A v 2 (-)

33 G. Wang et al [STAR Coll], arxiv:1210.5498 [nucl-ex] Testing the CMW at RHIC

34 CME @ Quark Matter 2014: ALICE Coll, Talk by R.Belmont ALICE Coll. at the LHC

35 CME @ Quark Matter 2014: STAR Coll, Talk by Q-Y Shou ALICE Coll, Talk by R.Belmont

36 Exciting the CMW by electromagnetic fields M.Stephanov, H.-U.Yee, arxiv:1304.6410 The first numerical simulation of CMHD! M.Hongo, Y.Hirono, T.Hirano, arxiv: 1309.2823

Dirac and Weyl semimetals

The discovery of Dirac semimetals 3D chiral materials Z.K.Liu et al., Science 343 p.864 (Feb 21, 2014)

The discovery of Dirac semimetals 3D chiral materials Z.K.Liu et al., Science 343 p.864 (Feb 21, 2014) Ongoing experimental studies of the Chiral Magnetic Effect

Chiral electronics 40 quantum amplifier - sensor of ultra- weak magnetic field DK, H.-U.Yee, Phys.Rev.B 88(2013) 115119 Dirac semimetal The Kirchhoffs law for this circuit possesses an instability

Summary Interplay of topology, anomalies and magnetic field leads to the Chiral Magnetic Effect; confirmed by lattice QCD x QED, evidence from RHIC and LHC CME and related anomaly-induced phenomena are an integral part of relativistic hydrodynamics (Chiral MagnetoHydroDynamics) Ongoing experimental studies of CME in Dirac semimetals; potential applications

The Chern-Simons diffusion rate in an external magnetic field 42 G. Basar, DK, arXiv:1202.2161 (PRD12) strongly coupled N=4 SYM plasma in an external U(1) R magnetic field through holography Dual geometry: Constant magnetic flux in x 3 direction: start with a general 5D metric and look for asymptotically AdS 5 solutions of Einstein-Maxwell equations with a horizon solutions interpolate between BTZ black hole x T 2 (small r) and AdS 5 (large r) RG flow from D=3+1 CFT at short distances, and D=1+1 CFT at large distances E.DHoker, P.Krauss, arXiv:0908.3875

Documents

1 The chiral magnetic effect: from quark-gluon plasma to Dirac semimetals D. Kharzeev High Energy Physics in the LHC Era, Valparaiso, Chile, 2012 “Quarks