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**The chiral magnetic effect: from quark-gluon plasma **

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

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**What is Chiral Magnetic Effect?**

Chirality imbalance + Magnetic field = Electric current Talks at “Quarks 2014”: V. Braguta, T. Kalaydzhyan, A. Kotov 2

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Quantum anomalies 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 if A, V are background fields, V is not conserved! V V 3

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**Quantum anomalies In classical background fields (E and B), chiral**

anomaly induces a collective motion in the Dirac sea A 4

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**Chiral Magnetic Effect in a chirally imbalanced plasma**

Fukushima, DK, Warringa, PRD‘08 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

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**Some of the earlier work on P-odd currents**

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 6

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**Chiral magnetic conductivity: discrete symmetries**

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

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**Systematics of anomalous conductivities**

Magnetic field Vorticity Vector current Axial current 8

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**Heavy ion collisions as a source of the strongest magnetic fields available in the Laboratory**

DK, McLerran, Warringa, Nucl Phys A803(2008)227 46

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**Heavy ion collisions: the strongest magnetic **

field ever achieved in the laboratory 47

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**Magnetic fields in heavy ion collisions**

In a conducting plasma, Faraday induction can make the field long-lived K.Tuchin, arXiv: , U.Gursoy, DK, K. Rajagopal, arXiv: L.McLerran,V.Skokov arXiv: 46

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**Magnetic fields in heavy ion collisions**

U.Gursoy, DK, K. Rajagopal, arXiv: Observable effects on directed flow of charged hadrons: Faraday + Hall Faraday 46

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**“Numerical evidence for chiral magnetic effect **

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

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**“Chiral magnetic effect in 2+1 flavor QCD+QED”,**

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

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**Electric dipole moment of QCD instanton in an external magnetic field**

B>0 G. Basar, G. Dunne, DK, arXiv: [hep-th] B=0 Quark zero mode density Topological charge density Asymmetry between left and right modes induces the e.d.m. in an external B

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Arxiv:

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**No sign problem for the chiral chemical potential - direct lattice studies are possible**

Fukushima, DK, Warringa, PRD‘08 17

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**+ Talks by V. Braguta and A. Kotov**

arXiv: , PRL 18

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**The Chern-Simons diffusion rate in an external magnetic field**

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

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**Holographic chiral magnetic effect: the strong coupling regime (AdS/CFT)**

Weak coupling Strong coupling H.-U. Yee, arXiv: , JHEP 0911:085, 2009; V. Rubakov, arXiv: , ... D.K., H. Warringa Phys Rev D80 (2009) A. Rebhan, A.Schmitt, S.Stricker JHEP 0905, 084 (2009), G.Lifshytz, M.Lippert, arXiv: ;.A. Gorsky, P. Kopnin, A. Zayakin, arXiv: , T. Kalaydzhyan, I. Kirsch ‘11,.. CME persists at strong coupling - hydrodynamical formulation?

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**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

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

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Chiral MagnetoHydroDynamics (CMHD) - relativistic hydrodynamics with triangle anomalies and external electromagnetic fields 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, ; 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 23 Many new anomaly-induced phenomena!

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**Is there another guiding principle?**

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

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**No entropy production from T-even anomalous terms**

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

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**No entropy production from P-odd anomalous terms**

DK and H.-U. Yee, Mirror reflection: entropy decreases ? Entropy grows Decrease is ruled out by 2nd law of thermodynamics 26

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**No entropy production from T-even anomalous terms**

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, 27

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**The fluid/gravity correspondence**

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, ; N. Banerjee et al, Other holographic checks work as well: It works 28 DK and H.-U. Yee,

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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

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**The CME in relativistic hydrodynamics: The Chiral Magnetic Wave**

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

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**The Chiral Magnetic Wave**

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

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**Testing the Chiral Magnetic Wave**

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, v2(-) > v2(+); at A<0, v2(+) > v2(-) Y.Burnier, DK, J.Liao, H.Yee, PRL 2011

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**Testing the CMW at RHIC G. Wang et al [STAR Coll],**

arxiv: [nucl-ex] Testing the CMW at RHIC

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**CME @ Quark Matter 2014: ALICE Coll. at the LHC ALICE Coll,**

Talk by R.Belmont

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**CME @ Quark Matter 2014: STAR Coll, Talk by Q-Y Shou ALICE Coll,**

Talk by R.Belmont

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**Exciting the CMW by electromagnetic fields**

M.Stephanov, H.-U.Yee, arxiv: The first numerical simulation of CMHD! M.Hongo, Y.Hirono, T.Hirano, arxiv:

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**Dirac and Weyl semimetals**

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**The discovery of Dirac semimetals – 3D chiral materials**

Trisodium bismuthide Z.K.Liu et al., Science 343 p.864 (Feb 21, 2014)

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**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

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**Chiral electronics quantum amplifier - sensor of ultra-weak**

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

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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

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**The Chern-Simons diffusion rate in an external magnetic field**

strongly coupled N=4 SYM plasma in an external U(1)R magnetic field through holography Dual geometry: Constant magnetic flux in x3 direction: start with a general 5D metric and look for asymptotically AdS5 solutions of Einstein-Maxwell equations with a horizon solutions interpolate between BTZ black hole x T2 (small r) and AdS5 (large r) RG flow from D=3+1 CFT at short distances, and D=1+1 CFT at large distances G. Basar, DK, arXiv: (PRD’12) E.D’Hoker, P.Krauss, arXiv:

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