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The chiral magnetic effect: from quark-gluon plasma to Dirac semimetals

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. What is Chiral Magnetic Effect?. C hirality imbalance + M agnetic field =

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The chiral magnetic effect: from quark-gluon plasma to Dirac semimetals

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  1. 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

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

  3. 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

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

  5. Chiral Magnetic Effectin 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

  6. Some of the earlier work onP-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

  7. 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

  8. Systematics of anomalous conductivities Magnetic field Vorticity Vector current Axial current 8

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

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

  11. 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

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

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

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

  15. Electric dipole moment of QCD instantonin an external magnetic field B>0 G. Basar, G. Dunne, DK, arXiv:1112.0532 [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

  16. Arxiv:1401.4141

  17. No sign problem for the chiral chemical potential - direct lattice studies are possible Fukushima, DK, Warringa, PRD‘08 17

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

  19. 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:1202.2161 weak field: strong field increases the rate: 19 dimensional reduction

  20. Holographic chiral magnetic effect:the strong coupling regime (AdS/CFT) Weak coupling Strong coupling H.-U. Yee, arXiv:0908.4189, JHEP 0911:085, 2009; V. Rubakov, arXiv:1005.1888, ... D.K., H. Warringa Phys Rev D80 (2009) 034028 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?

  21. 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

  22. 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:0906.5044 Constraining the new anomalous transport coefficients: positivity of the entropy production rate, CME (for chirally imbalanced matter) 22

  23. 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, 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 23 Many new anomaly-induced phenomena!

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

  25. No entropy production from T-even anomalous terms DK and H.-U. Yee, 1105.6360 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

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

  27. 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, 1105.6360 27

  28. 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, 0809.2488; N. Banerjee et al, 0809.2596 Other holographic checks work as well: It works 28 DK and H.-U. Yee, 1105.6360

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

  30. The CME in relativistic hydrodynamics: The Chiral Magnetic Wave DK, H.-U. Yee, arXiv:1012.6026 [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

  31. 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:1012.6026 [hep-th], PRD 31

  32. 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

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

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

  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

  37. Dirac and Weyl semimetals

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

  39. 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

  40. Chiral electronics 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) 115119 40

  41. 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

  42. 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:1202.2161 (PRD’12) E.D’Hoker, P.Krauss, arXiv:0908.3875

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