Advertisement

Nonlinear chiral transport from holography

  • Yanyan Bu
  • Tuna DemircikEmail author
  • Michael Lublinsky
Open Access
Regular Article - Theoretical Physics
  • 15 Downloads

Abstract

Nonlinear transport phenomena induced by the chiral anomaly are explored within a 4D field theory defined holographically as U(1)V × U(1)A Maxwell-Chern-Simons theory in Schwarzschild-AdS5. First, in presence of external electromagnetic fields, a general form of vector and axial currents is derived. Then, within the gradient expansion up to third order, we analytically compute all (over 50) transport coefficients. A wealth of higher order (nonlinear) transport phenomena induced by chiral anomaly are found beyond the Chiral Magnetic and Chiral Separation Effects. Some of the higher order terms are relaxation time corrections to the lowest order nonlinear effects. The charge diffusion constant and dispersion relation of the Chiral Magnetic Wave are found to receive anomaly-induced non-linear corrections due to e/m background fields. Furthermore, there emerges a new gapless mode, which we refer to as Chiral Hall Density Wave, propagating along the background Poynting vector.

Keywords

AdS-CFT Correspondence Gauge-gravity correspondence Holography and quark-gluon plasmas 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    L. Landau and E. Lifshitz, Fluid Mechanics, Volume 6, Elsevier Science, (2013).Google Scholar
  2. [2]
    D. Forster, Hydrodynamic fluctuations, broken symmetry, and correlation functions, CRC Press, (1975).Google Scholar
  3. [3]
    M. Lublinsky and E. Shuryak, How much entropy is produced in strongly coupled quark-gluon Plasma (sQGP) by dissipative effects?, Phys. Rev. C 76 (2007) 021901 [arXiv:0704.1647] [INSPIRE].ADSGoogle Scholar
  4. [4]
    M. Lublinsky and E. Shuryak, Improved Hydrodynamics from the AdS/CFT, Phys. Rev. D 80 (2009) 065026 [arXiv:0905.4069] [INSPIRE].ADSGoogle Scholar
  5. [5]
    Y. Bu and M. Lublinsky, All order linearized hydrodynamics from fluid-gravity correspondence, Phys. Rev. D 90 (2014) 086003 [arXiv:1406.7222] [INSPIRE].ADSzbMATHGoogle Scholar
  6. [6]
    Y. Bu and M. Lublinsky, Linearized fluid/gravity correspondence: from shear viscosity to all order hydrodynamics, JHEP 11 (2014) 064 [arXiv:1409.3095] [INSPIRE].ADSzbMATHGoogle Scholar
  7. [7]
    Y. Bu and M. Lublinsky, Linearly resummed hydrodynamics in a weakly curved spacetime, JHEP 04 (2015) 136 [arXiv:1502.08044] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  8. [8]
    Y. Bu, M. Lublinsky and A. Sharon, Hydrodynamics dual to Einstein-Gauss-Bonnet gravity: all-order gradient resummation, JHEP 06 (2015) 162 [arXiv:1504.01370] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  9. [9]
    I. Müller, Zum paradoxon der wärmeleitungstheorie, Z. Phys. 198 (1967) 329.ADSzbMATHGoogle Scholar
  10. [10]
    W. Israel, Nonstationary irreversible thermodynamics: A causal relativistic theory, Annals Phys. 100 (1976) 310 [INSPIRE].ADSMathSciNetGoogle Scholar
  11. [11]
    W. Israel and J. Stewart, Thermodynamics of nonstationary and transient effects in a relativistic gas, Phys. Lett. A 58 (1976) 213.ADSGoogle Scholar
  12. [12]
    W. Israel and J.M. Stewart, Transient relativistic thermodynamics and kinetic theory, Annals Phys. 118 (1979) 341 [INSPIRE].ADSMathSciNetGoogle Scholar
  13. [13]
    M.P. Heller, R.A. Janik and P. Witaszczyk, Hydrodynamic Gradient Expansion in Gauge Theory Plasmas, Phys. Rev. Lett. 110 (2013) 211602 [arXiv:1302.0697] [INSPIRE].ADSGoogle Scholar
  14. [14]
    M.P. Heller and M. Spaliński, Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation, Phys. Rev. Lett. 115 (2015) 072501 [arXiv:1503.07514] [INSPIRE].ADSGoogle Scholar
  15. [15]
    S. Grozdanov and N. Kaplis, Constructing higher-order hydrodynamics: The third order, Phys. Rev. D 93 (2016) 066012 [arXiv:1507.02461] [INSPIRE].ADSMathSciNetGoogle Scholar
  16. [16]
    P. Romatschke, Do nuclear collisions create a locally equilibrated quark-gluon plasma?, Eur. Phys. J. C 77 (2017) 21 [arXiv:1609.02820] [INSPIRE].ADSGoogle Scholar
  17. [17]
    P. Romatschke, Relativistic Fluid Dynamics Far From Local Equilibrium, Phys. Rev. Lett. 120 (2018) 012301 [arXiv:1704.08699] [INSPIRE].ADSGoogle Scholar
  18. [18]
    M. Spaliński, On the hydrodynamic attractor of Yang-Mills plasma, Phys. Lett. B 776 (2018) 468 [arXiv:1708.01921] [INSPIRE].ADSMathSciNetGoogle Scholar
  19. [19]
    P. Romatschke, Relativistic Hydrodynamic Attractors with Broken Symmetries: Non-Conformal and Non-Homogeneous, JHEP 12 (2017) 079 [arXiv:1710.03234] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  20. [20]
    W. Florkowski, M.P. Heller and M. Spaliński, New theories of relativistic hydrodynamics in the LHC era, Rept. Prog. Phys. 81 (2018) 046001 [arXiv:1707.02282] [INSPIRE].ADSMathSciNetGoogle Scholar
  21. [21]
    G.S. Denicol and J. Noronha, Hydrodynamic attractor and the fate of perturbative expansions in Gubser flow, arXiv:1804.04771 [INSPIRE].
  22. [22]
    A. Behtash, C.N. Cruz-Camacho and M. Martinez, Far-from-equilibrium attractors and nonlinear dynamical systems approach to the Gubser flow, Phys. Rev. D 97 (2018) 044041 [arXiv:1711.01745] [INSPIRE].ADSMathSciNetGoogle Scholar
  23. [23]
    A. Behtash, S. Kamata, M. Martinez and C.N. Cruz-Camacho, Non-perturbative rheological behavior of a far-from-equilibrium expanding plasma, arXiv:1805.07881 [INSPIRE].
  24. [24]
    Y. Bu, M. Lublinsky and A. Sharon, Anomalous transport from holography: Part I, JHEP 11 (2016) 093 [arXiv:1608.08595] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  25. [25]
    Y. Bu, M. Lublinsky and A. Sharon, Anomalous transport from holography: Part II, Eur. Phys. J. C 77 (2017) 194 [arXiv:1609.09054] [INSPIRE].ADSzbMATHGoogle Scholar
  26. [26]
    V.A. Kuzmin, V.A. Rubakov and M.E. Shaposhnikov, On the Anomalous Electroweak Baryon Number Nonconservation in the Early Universe, Phys. Lett. 155B (1985) 36 [INSPIRE].ADSGoogle Scholar
  27. [27]
    A. Vilenkin and D.A. Leahy, Parity non-conservation and the origin of cosmic magnetic fields, Astrophys. J. 254 (1982) 77 [INSPIRE].ADSGoogle Scholar
  28. [28]
    V.A. Rubakov and M.E. Shaposhnikov, Electroweak baryon number nonconservation in the early universe and in high-energy collisions, Usp. Fiz. Nauk 166 (1996) 493 [hep-ph/9603208] [INSPIRE].
  29. [29]
    D. Grasso and H.R. Rubinstein, Magnetic fields in the early universe, Phys. Rept. 348 (2001) 163 [astro-ph/0009061] [INSPIRE].
  30. [30]
    M. Giovannini, The magnetized universe, Int. J. Mod. Phys. D 13 (2004) 391 [astro-ph/0312614] [INSPIRE].
  31. [31]
    D.E. Kharzeev, Topology, magnetic field and strongly interacting matter, Ann. Rev. Nucl. Part. Sci. 65 (2015) 193 [arXiv:1501.01336] [INSPIRE].ADSGoogle Scholar
  32. [32]
    D.E. Kharzeev, The Chiral Magnetic Effect and Anomaly-Induced Transport, Prog. Part. Nucl. Phys. 75 (2014) 133 [arXiv:1312.3348] [INSPIRE].ADSGoogle Scholar
  33. [33]
    X.-G. Huang, Electromagnetic fields and anomalous transports in heavy-ion collisions — A pedagogical review, Rept. Prog. Phys. 79 (2016) 076302 [arXiv:1509.04073] [INSPIRE].ADSGoogle Scholar
  34. [34]
    ALICE collaboration, Charge-dependent flow and the search for the chiral magnetic wave in Pb-Pb collisions at \( \sqrt{s_{\mathrm{NN}}}=2.76 \) TeV, Phys. Rev. C 93 (2016) 044903 [arXiv:1512.05739] [INSPIRE].
  35. [35]
    CMS collaboration, Observation of charge-dependent azimuthal correlations in p-Pb collisions and its implication for the search for the chiral magnetic effect, Phys. Rev. Lett. 118 (2017) 122301 [arXiv:1610.00263] [INSPIRE].
  36. [36]
    CMS collaboration, Constraints on the chiral magnetic effect using charge-dependent azimuthal correlations in pPb and PbPb collisions at the CERN Large Hadron Collider, Phys. Rev. C 97 (2018) 044912 [arXiv:1708.01602] [INSPIRE].
  37. [37]
    CMS collaboration, Challenges to the chiral magnetic wave using charge-dependent azimuthal anisotropies in pPb and PbPb collisions at \( \sqrt{s_{\mathrm{NN}}}=5.02 \) TeV, arXiv:1708.08901 [INSPIRE].
  38. [38]
    V. Koch et al., Status of the chiral magnetic effect and collisions of isobars, Chin. Phys. C 41 (2017) 072001 [arXiv:1608.00982] [INSPIRE].ADSGoogle Scholar
  39. [39]
    Z.K. Liu et al., Discovery of a Three-Dimensional Topological Dirac Semimetal, Na 3 Bi, Science 343 (2015) 864.ADSGoogle Scholar
  40. [40]
    B.Q. Lv et al., Experimental discovery of Weyl semimetal TaAs, Phys. Rev. X 5 (2015) 031013 [arXiv:1502.04684] [INSPIRE].Google Scholar
  41. [41]
    S.Y. Xu et al., Discovery of a Weyl Fermion semimetal and topological Fermi arcs, Science 349 (2015) 613 [INSPIRE].ADSGoogle Scholar
  42. [42]
    O. Vafek and A. Vishwanath, Dirac Fermions in Solids: From High-Tc cuprates and Graphene to Topological Insulators and Weyl Semimetals, Ann. Rev. Condensed Matter Phys. 5 (2014) 83 [arXiv:1306.2272] [INSPIRE].ADSGoogle Scholar
  43. [43]
    Q. Li et al., Observation of the chiral magnetic effect in ZrTe 5, Nature Phys. 12 (2016) 550 [arXiv:1412.6543] [INSPIRE].ADSGoogle Scholar
  44. [44]
    X. Huang et al., Observation of the Chiral-Anomaly-Induced Negative Magnetoresistance in 3D Weyl Semimetal TaAs, Phys. Rev. X 5 (2015) 031023 [arXiv:1503.01304] [INSPIRE].Google Scholar
  45. [45]
    H. Li et al., Negative Magnetoresistance in Dirac Semimetal Cd 3 As 2, Nat. Commun. 7 (2016) 10301 [arXiv:1507.06470].ADSGoogle Scholar
  46. [46]
    K. Landsteiner, E. Megias and F. Pena-Benitez, Anomalous Transport from Kubo Formulae, Lect. Notes Phys. 871 (2013) 433 [arXiv:1207.5808].ADSGoogle Scholar
  47. [47]
    K. Landsteiner, Y. Liu and Y.-W. Sun, Negative magnetoresistivity in chiral fluids and holography, JHEP 03 (2015) 127 [arXiv:1410.6399] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  48. [48]
    A. Jimenez-Alba, K. Landsteiner, Y. Liu and Y.-W. Sun, Anomalous magnetoconductivity and relaxation times in holography, JHEP 07 (2015) 117 [arXiv:1504.06566] [INSPIRE].ADSGoogle Scholar
  49. [49]
    K. Landsteiner and Y. Liu, The holographic Weyl semi-metal, Phys. Lett. B 753 (2016) 453 [arXiv:1505.04772] [INSPIRE].ADSzbMATHGoogle Scholar
  50. [50]
    A. Vilenkin, Equilibrium parity violating current in a magnetic field, Phys. Rev. D 22 (1980) 3080 [INSPIRE].ADSGoogle Scholar
  51. [51]
    K. Fukushima, D.E. Kharzeev and H.J. Warringa, The Chiral Magnetic Effect, Phys. Rev. D 78 (2008) 074033 [arXiv:0808.3382] [INSPIRE].ADSGoogle Scholar
  52. [52]
    D.E. Kharzeev and H.J. Warringa, Chiral Magnetic conductivity, Phys. Rev. D 80 (2009) 034028 [arXiv:0907.5007] [INSPIRE].ADSGoogle Scholar
  53. [53]
    K. Fukushima, D.E. Kharzeev and H.J. Warringa, Real-time dynamics of the Chiral Magnetic Effect, Phys. Rev. Lett. 104 (2010) 212001 [arXiv:1002.2495] [INSPIRE].ADSGoogle Scholar
  54. [54]
    D. Hou, H. Liu and H.-c. Ren, Some Field Theoretic Issues Regarding the Chiral Magnetic Effect, JHEP 05 (2011) 046 [arXiv:1103.2035] [INSPIRE].ADSzbMATHGoogle Scholar
  55. [55]
    D. Satow and H.-U. Yee, Chiral Magnetic Effect at Weak Coupling with Relaxation Dynamics, Phys. Rev. D 90 (2014) 014027 [arXiv:1406.1150] [INSPIRE].ADSGoogle Scholar
  56. [56]
    H.-U. Yee, Chiral Magnetic and Vortical Effects in Higher Dimensions at Weak Coupling, Phys. Rev. D 90 (2014) 065021 [arXiv:1406.3584] [INSPIRE].ADSGoogle Scholar
  57. [57]
    A. Jimenez-Alba and H.-U. Yee, Second order transport coefficient from the chiral anomaly at weak coupling: Diagrammatic resummation, Phys. Rev. D 92 (2015) 014023 [arXiv:1504.05866] [INSPIRE].ADSGoogle Scholar
  58. [58]
    G.M. Newman, Anomalous hydrodynamics, JHEP 01 (2006) 158 [hep-ph/0511236] [INSPIRE].
  59. [59]
    H.-U. Yee, Holographic Chiral Magnetic Conductivity, JHEP 11 (2009) 085 [arXiv:0908.4189] [INSPIRE].ADSGoogle Scholar
  60. [60]
    A. Rebhan, A. Schmitt and S.A. Stricker, Anomalies and the chiral magnetic effect in the Sakai-Sugimoto model, JHEP 01 (2010) 026 [arXiv:0909.4782] [INSPIRE].ADSzbMATHGoogle Scholar
  61. [61]
    Y. Matsuo, S.-J. Sin, S. Takeuchi and T. Tsukioka, Magnetic conductivity and Chern-Simons Term in Holographic Hydrodynamics of Charged AdS Black Hole, JHEP 04 (2010) 071 [arXiv:0910.3722] [INSPIRE].ADSzbMATHGoogle Scholar
  62. [62]
    A. Gorsky, P.N. Kopnin and A.V. Zayakin, On the Chiral Magnetic Effect in Soft-Wall AdS/QCD, Phys. Rev. D 83 (2011) 014023 [arXiv:1003.2293] [INSPIRE].ADSGoogle Scholar
  63. [63]
    V.A. Rubakov, On chiral magnetic effect and holography, arXiv:1005.1888 [INSPIRE].
  64. [64]
    A. Gynther, K. Landsteiner, F. Pena-Benitez and A. Rebhan, Holographic Anomalous Conductivities and the Chiral Magnetic Effect, JHEP 02 (2011) 110 [arXiv:1005.2587] [INSPIRE].ADSzbMATHGoogle Scholar
  65. [65]
    I. Amado, K. Landsteiner and F. Pena-Benitez, Anomalous transport coefficients from Kubo formulas in Holography, JHEP 05 (2011) 081 [arXiv:1102.4577] [INSPIRE].ADSzbMATHGoogle Scholar
  66. [66]
    T. Kalaydzhyan and I. Kirsch, Fluid/gravity model for the chiral magnetic effect, Phys. Rev. Lett. 106 (2011) 211601 [arXiv:1102.4334] [INSPIRE].ADSGoogle Scholar
  67. [67]
    C. Hoyos, T. Nishioka and A. O’Bannon, A Chiral Magnetic Effect from AdS/CFT with Flavor, JHEP 10 (2011) 084 [arXiv:1106.4030] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  68. [68]
    Y.-P. Hu, P. Sun and J.-H. Zhang, Hydrodynamics with conserved current via AdS/CFT correspondence in the Maxwell-Gauss-Bonnet gravity, Phys. Rev. D 83 (2011) 126003 [arXiv:1103.3773] [INSPIRE].ADSGoogle Scholar
  69. [69]
    Y.-P. Hu and C. Park, Chern-Simons effect on the dual hydrodynamics in the Maxwell-Gauss-Bonnet gravity, Phys. Lett. B 714 (2012) 324 [arXiv:1112.4227] [INSPIRE].ADSMathSciNetGoogle Scholar
  70. [70]
    X. Bai, Y.-P. Hu, B.-H. Lee and Y.-L. Zhang, Holographic Charged Fluid with Anomalous Current at Finite Cutoff Surface in Einstein-Maxwell Gravity, JHEP 11 (2012) 054 [arXiv:1207.5309] [INSPIRE].ADSGoogle Scholar
  71. [71]
    S. Lin and H.-U. Yee, Out-of-Equilibrium Chiral Magnetic Effect at Strong Coupling, Phys. Rev. D 88 (2013) 025030 [arXiv:1305.3949] [INSPIRE].ADSGoogle Scholar
  72. [72]
    I. Iatrakis, S. Lin and Y. Yin, The anomalous transport of axial charge: topological vs non-topological fluctuations, JHEP 09 (2015) 030 [arXiv:1506.01384] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  73. [73]
    S. Grozdanov and N. Poovuttikul, Universality of anomalous conductivities in theories with higher-derivative holographic duals, JHEP 09 (2016) 046 [arXiv:1603.08770] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  74. [74]
    M. Ammon, M. Kaminski, R. Koirala, J. Leiber and J. Wu, Quasinormal modes of charged magnetic black branes & chiral magnetic transport, JHEP 04 (2017) 067 [arXiv:1701.05565] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  75. [75]
    J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  76. [76]
    S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].ADSzbMATHGoogle Scholar
  77. [77]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  78. [78]
    D.T. Son and P. Surowka, Hydrodynamics with Triangle Anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [INSPIRE].ADSMathSciNetGoogle Scholar
  79. [79]
    A.V. Sadofyev and M.V. Isachenkov, The chiral magnetic effect in hydrodynamical approach, Phys. Lett. B 697 (2011) 404 [arXiv:1010.1550] [INSPIRE].ADSGoogle Scholar
  80. [80]
    D.T. Son and N. Yamamoto, Berry Curvature, Triangle Anomalies and the Chiral Magnetic Effect in Fermi Liquids, Phys. Rev. Lett. 109 (2012) 181602 [arXiv:1203.2697] [INSPIRE].ADSGoogle Scholar
  81. [81]
    M.A. Stephanov and Y. Yin, Chiral Kinetic Theory, Phys. Rev. Lett. 109 (2012) 162001 [arXiv:1207.0747] [INSPIRE].ADSGoogle Scholar
  82. [82]
    D.T. Son and N. Yamamoto, Kinetic theory with Berry curvature from quantum field theories, Phys. Rev. D 87 (2013) 085016 [arXiv:1210.8158] [INSPIRE].ADSGoogle Scholar
  83. [83]
    J.-H. Gao, Z.-T. Liang, S. Pu, Q. Wang and X.-N. Wang, Chiral Anomaly and Local Polarization Effect from Quantum Kinetic Approach, Phys. Rev. Lett. 109 (2012) 232301 [arXiv:1203.0725] [INSPIRE].ADSGoogle Scholar
  84. [84]
    J.-W. Chen, S. Pu, Q. Wang and X.-N. Wang, Berry Curvature and Four-Dimensional Monopoles in the Relativistic Chiral Kinetic Equation, Phys. Rev. Lett. 110 (2013) 262301 [arXiv:1210.8312] [INSPIRE].ADSGoogle Scholar
  85. [85]
    P.V. Buividovich, M.N. Chernodub, E.V. Luschevskaya and M.I. Polikarpov, Numerical evidence of chiral magnetic effect in lattice gauge theory, Phys. Rev. D 80 (2009) 054503 [arXiv:0907.0494] [INSPIRE].ADSGoogle Scholar
  86. [86]
    M. Abramczyk, T. Blum, G. Petropoulos and R. Zhou, Chiral magnetic effect in 2+1 flavor QCD+QED, PoS(LAT2009)181 (2009) [arXiv:0911.1348] [INSPIRE].
  87. [87]
    K. Fukushima, D.E. Kharzeev and H.J. Warringa, Electric-current Susceptibility and the Chiral Magnetic Effect, Nucl. Phys. A 836 (2010) 311 [arXiv:0912.2961] [INSPIRE].ADSGoogle Scholar
  88. [88]
    V.V. Braguta, P.V. Buividovich, T. Kalaydzhyan, S.V. Kuznetsov and M.I. Polikarpov, The Chiral Magnetic Effect and chiral symmetry breaking in SU(3) quenched lattice gauge theory, Phys. Atom. Nucl. 75 (2012) 488 [arXiv:1011.3795] [INSPIRE].ADSGoogle Scholar
  89. [89]
    A. Yamamoto, Chiral magnetic effect in lattice QCD with a chiral chemical potential, Phys. Rev. Lett. 107 (2011) 031601 [arXiv:1105.0385] [INSPIRE].ADSGoogle Scholar
  90. [90]
    V. Braguta, M.N. Chernodub, K. Landsteiner, M.I. Polikarpov and M.V. Ulybyshev, Numerical evidence of the axial magnetic effect, Phys. Rev. D 88 (2013) 071501 [arXiv:1303.6266] [INSPIRE].ADSGoogle Scholar
  91. [91]
    N. Yamamoto, Generalized Bloch theorem and chiral transport phenomena, Phys. Rev. D 92 (2015) 085011 [arXiv:1502.01547] [INSPIRE].ADSGoogle Scholar
  92. [92]
    M.A. Zubkov, Absence of equilibrium chiral magnetic effect, Phys. Rev. D 93 (2016) 105036 [arXiv:1605.08724] [INSPIRE].ADSMathSciNetGoogle Scholar
  93. [93]
    D.T. Son and A.R. Zhitnitsky, Quantum anomalies in dense matter, Phys. Rev. D 70 (2004) 074018 [hep-ph/0405216] [INSPIRE].
  94. [94]
    M.A. Metlitski and A.R. Zhitnitsky, Anomalous axion interactions and topological currents in dense matter, Phys. Rev. D 72 (2005) 045011 [hep-ph/0505072] [INSPIRE].
  95. [95]
    D.E. Kharzeev and H.-U. Yee, Chiral Magnetic Wave, Phys. Rev. D 83 (2011) 085007 [arXiv:1012.6026] [INSPIRE].ADSGoogle Scholar
  96. [96]
    Y. Bu, T. Demircik and M. Lublinsky, Gradient resummation for nonlinear chiral transport: an insight from holography, arXiv:1807.11908 [INSPIRE].
  97. [97]
    M. Joyce and M.E. Shaposhnikov, Primordial magnetic fields, right-handed electrons and the Abelian anomaly, Phys. Rev. Lett. 79 (1997) 1193 [astro-ph/9703005] [INSPIRE].
  98. [98]
    A. Boyarsky, J. Fröhlich and O. Ruchayskiy, Self-consistent evolution of magnetic fields and chiral asymmetry in the early Universe, Phys. Rev. Lett. 108 (2012) 031301 [arXiv:1109.3350] [INSPIRE].ADSGoogle Scholar
  99. [99]
    C. Manuel and J.M. Torres-Rincon, Dynamical evolution of the chiral magnetic effect: Applications to the quark-gluon plasma, Phys. Rev. D 92 (2015) 074018 [arXiv:1501.07608] [INSPIRE].ADSGoogle Scholar
  100. [100]
    A. Boyarsky, J. Fröhlich and O. Ruchayskiy, Magnetohydrodynamics of Chiral Relativistic Fluids, Phys. Rev. D 92 (2015) 043004 [arXiv:1504.04854] [INSPIRE].ADSGoogle Scholar
  101. [101]
    Y. Hirono, D. Kharzeev and Y. Yin, Self-similar inverse cascade of magnetic helicity driven by the chiral anomaly, Phys. Rev. D 92 (2015) 125031 [arXiv:1509.07790] [INSPIRE].ADSGoogle Scholar
  102. [102]
    A. Avdoshkin, V.P. Kirilin, A.V. Sadofyev and V.I. Zakharov, On consistency of hydrodynamic approximation for chiral media, Phys. Lett. B 755 (2016) 1 [arXiv:1402.3587] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  103. [103]
    J.-W. Chen, T. Ishii, S. Pu and N. Yamamoto, Nonlinear Chiral Transport Phenomena, Phys. Rev. D 93 (2016) 125023 [arXiv:1603.03620] [INSPIRE].ADSMathSciNetGoogle Scholar
  104. [104]
    E.V. Gorbar, I.A. Shovkovy, S. Vilchinskii, I. Rudenok, A. Boyarsky and O. Ruchayskiy, Anomalous Maxwell equations for inhomogeneous chiral plasma, Phys. Rev. D 93 (2016) 105028 [arXiv:1603.03442] [INSPIRE].ADSMathSciNetGoogle Scholar
  105. [105]
    O.F. Dayi and E. Kilinçarslan, Nonlinear Chiral Plasma Transport in Rotating Coordinates, Phys. Rev. D 96 (2017) 043514 [arXiv:1705.01267] [INSPIRE].ADSMathSciNetGoogle Scholar
  106. [106]
    Y. Hidaka, S. Pu and D.-L. Yang, Nonlinear Responses of Chiral Fluids from Kinetic Theory, Phys. Rev. D 97 (2018) 016004 [arXiv:1710.00278] [INSPIRE].ADSGoogle Scholar
  107. [107]
    D.E. Kharzeev and H.-U. Yee, Anomalies and time reversal invariance in relativistic hydrodynamics: the second order and higher dimensional formulations, Phys. Rev. D 84 (2011) 045025 [arXiv:1105.6360] [INSPIRE].ADSGoogle Scholar
  108. [108]
    E. Megias and F. Pena-Benitez, Holographic Gravitational Anomaly in First and Second Order Hydrodynamics, JHEP 05 (2013) 115 [arXiv:1304.5529] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  109. [109]
    U. Gürsoy and J. Tarrio, Horizon universality and anomalous conductivities, JHEP 10 (2015) 058 [arXiv:1410.1306] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  110. [110]
    U. Gürsoy and A. Jansen, (Non)renormalization of Anomalous Conductivities and Holography, JHEP 10 (2014) 092 [arXiv:1407.3282] [INSPIRE].
  111. [111]
    Y. Bu, M. Lublinsky and A. Sharon, U(1) current from the AdS/CFT: diffusion, conductivity and causality, JHEP 04 (2016) 136 [arXiv:1511.08789] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  112. [112]
    G. Basar and G.V. Dunne, Hydrodynamics, resurgence and transasymptotics, Phys. Rev. D 92 (2015) 125011 [arXiv:1509.05046] [INSPIRE].ADSGoogle Scholar
  113. [113]
    Y. Bu, R.-G. Cai, Q. Yang and Y.-L. Zhang, Holographic Charged Fluid with Chiral Electric Separation Effect, JHEP 09 (2018) 083 [arXiv:1803.08389] [INSPIRE].ADSMathSciNetGoogle Scholar
  114. [114]
    S. Li and H.-U. Yee, Relaxation times for chiral transport phenomena and spin polarization in a strongly coupled plasma, Phys. Rev. D 98 (2018) 056018 [arXiv:1805.04057] [INSPIRE].ADSGoogle Scholar
  115. [115]
    R.C. Myers, A.O. Starinets and R.M. Thomson, Holographic spectral functions and diffusion constants for fundamental matter, JHEP 11 (2007) 091 [arXiv:0706.0162] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  116. [116]
    S. Pu, S.-Y. Wu and D.-L. Yang, Chiral Hall Effect and Chiral Electric Waves, Phys. Rev. D 91 (2015) 025011 [arXiv:1407.3168] [INSPIRE].ADSGoogle Scholar
  117. [117]
    Y. Bu, T. Demircik and M. Lublinsky, Nonlinear chiral transport from holography: strong field limit, in preparation.Google Scholar
  118. [118]
    S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear Fluid Dynamics from Gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [INSPIRE].ADSGoogle Scholar
  119. [119]
    J. Erdmenger, M. Haack, M. Kaminski and A. Yarom, Fluid dynamics of R-charged black holes, JHEP 01 (2009) 055 [arXiv:0809.2488] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  120. [120]
    N. Banerjee, J. Bhattacharya, S. Bhattacharyya, S. Dutta, R. Loganayagam and P. Surowka, Hydrodynamics from charged black branes, JHEP 01 (2011) 094 [arXiv:0809.2596] [INSPIRE].ADSzbMATHGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of PhysicsHarbin Institute of TechnologyHarbinChina
  2. 2.Department of PhysicsBen-Gurion University of the NegevBeer-ShevaIsrael

Personalised recommendations