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Journal of High Energy Physics

, 2018:83 | Cite as

Holographic charged fluid with chiral electric separation effect

  • Yanyan Bu
  • Rong-Gen Cai
  • Qing Yang
  • Yun-Long Zhang
Open Access
Regular Article - Theoretical Physics
  • 24 Downloads

Abstract

Hydrodynamics with both vector and axial currents is under study within a holographic model, consisting of canonical U(1)V × U(1)A gauge fields in an asymptotically AdS5 black brane. When gravitational back-reaction is taken into account, the chiral electric separation effect (CESE), namely the generation of an axial current as the response to an external electric field, is realized naturally. Via fluid/gravity correspondence, all the first order transport coefficients in the hydrodynamic constitutive relations are evaluated analytically: they are functions of vector chemical potential μ, axial chemical potential μ5 and the fluid’s temperature T . Apart from the proportionality factor μμ5, the CESE conductivity is found to be dependent on the dimensionless quantities μ/T and μ5/T nontrivially. As a complementary study, frequency-dependent transport phenomena are revealed through linear response analysis, demonstrating perfect agreement with the results obtained from fluid/gravity correspondence.

Keywords

Holography and quark-gluon plasmas Holography and condensed matter physics (AdS/CMT) 

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]
    D. Kharzeev, Parity violation in hot QCD: Why it can happen and how to look for it, Phys. Lett. B 633 (2006) 260 [hep-ph/0406125] [INSPIRE].
  2. [2]
    D. Kharzeev and A. Zhitnitsky, Charge separation induced by P-odd bubbles in QCD matter, Nucl. Phys. A 797 (2007) 67 [arXiv:0706.1026] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    D.E. Kharzeev, L.D. McLerran and H.J. Warringa, The Effects of topological charge change in heavy ion collisions: ‘Event by event P and CP-violation’, Nucl. Phys. A 803 (2008) 227 [arXiv:0711.0950] [INSPIRE].
  4. [4]
    K. Fukushima, D.E. Kharzeev and H.J. Warringa, The Chiral Magnetic Effect, Phys. Rev. D 78 (2008) 074033 [arXiv:0808.3382] [INSPIRE].
  5. [5]
    J. Erdmenger, M. Haack, M. Kaminski and A. Yarom, Fluid dynamics of R-charged black holes, JHEP 01 (2009) 055 [arXiv:0809.2488] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    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].ADSCrossRefGoogle Scholar
  7. [7]
    D.T. Son and P. Surowka, Hydrodynamics with Triangle Anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    D.T. Son and A.R. Zhitnitsky, Quantum anomalies in dense matter, Phys. Rev. D 70 (2004) 074018 [hep-ph/0405216] [INSPIRE].
  9. [9]
    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].
  10. [10]
    D.E. Kharzeev and H.-U. Yee, Chiral Magnetic Wave, Phys. Rev. D 83 (2011) 085007 [arXiv:1012.6026] [INSPIRE].
  11. [11]
    Y. Burnier, D.E. Kharzeev, J. Liao and H.-U. Yee, Chiral magnetic wave at finite baryon density and the electric quadrupole moment of quark-gluon plasma in heavy ion collisions, Phys. Rev. Lett. 107 (2011) 052303 [arXiv:1103.1307] [INSPIRE].
  12. [12]
    D.E. Kharzeev and D.T. Son, Testing the chiral magnetic and chiral vortical effects in heavy ion collisions, Phys. Rev. Lett. 106 (2011) 062301 [arXiv:1010.0038] [INSPIRE].
  13. [13]
    A. Bzdak, V. Koch and J. Liao, Charge-Dependent Correlations in Relativistic Heavy Ion Collisions and the Chiral Magnetic Effect, Lect. Notes Phys. 871 (2013) 503 [arXiv:1207.7327] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    H.-U. Yee and Y. Yin, Realistic Implementation of Chiral Magnetic Wave in Heavy Ion Collisions, Phys. Rev. C 89 (2014) 044909 [arXiv:1311.2574] [INSPIRE].
  15. [15]
    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].
  16. [16]
    CMS collaboration, Observation of charge-dependent azimuthal correlations in p-P b collisions and its implication for the search for the chiral magnetic effect, Phys. Rev. Lett. 118 (2017) 122301 [arXiv:1610.00263] [INSPIRE].
  17. [17]
    CMS collaboration, Constraints on the chiral magnetic effect using charge-dependent azimuthal correlations in pP b and P bP b collisions at the CERN Large Hadron Collider, Phys. Rev. C 97 (2018) 044912 [arXiv:1708.01602] [INSPIRE].
  18. [18]
    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].
  19. [19]
    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].
  20. [20]
    H. Li et al., Negative Magnetoresistance in Dirac Semimetal Cd3As2, Nat. Commun. 7 (2016) 10301 [arXiv:1507.06470].ADSCrossRefGoogle Scholar
  21. [21]
    Q. Li et al., Observation of the chiral magnetic effect in ZrTe5, Nature Phys. 12 (2016) 550 [arXiv:1412.6543] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    D.E. Kharzeev, The Chiral Magnetic Effect and Anomaly-Induced Transport, Prog. Part. Nucl. Phys. 75 (2014) 133 [arXiv:1312.3348] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    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].ADSCrossRefGoogle Scholar
  24. [24]
    D.E. Kharzeev, J. Liao, S.A. Voloshin and G. Wang, Chiral magnetic and vortical effects in high-energy nuclear collisions — A status report, Prog. Part. Nucl. Phys. 88 (2016) 1 [arXiv:1511.04050] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    V. Koch et al., Status of the chiral magnetic effect and collisions of isobars, Chin. Phys. C 41 (2017) 072001 [arXiv:1608.00982] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    K. Landsteiner, Notes on Anomaly Induced Transport, Acta Phys. Polon. B 47 (2016) 2617 [arXiv:1610.04413] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    E.V. Gorbar, V.A. Miransky, I.A. Shovkovy and P.O. Sukhachov, Anomalous transport properties of Dirac and Weyl semimetals (Review Article), Low Temp. Phys. 44 (2018) 487 [arXiv:1712.08947] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    X.-G. Huang and J. Liao, Axial Current Generation from Electric Field: Chiral Electric Separation Effect, Phys. Rev. Lett. 110 (2013) 232302 [arXiv:1303.7192] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    Y. Jiang, X.-G. Huang and J. Liao, Chiral electric separation effect in the quark-gluon plasma, Phys. Rev. D 91 (2015) 045001 [arXiv:1409.6395] [INSPIRE].
  30. [30]
    S. Pu, S.-Y. Wu and D.-L. Yang, Holographic Chiral Electric Separation Effect, Phys. Rev. D 89 (2014) 085024 [arXiv:1401.6972] [INSPIRE].
  31. [31]
    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].
  32. [32]
    T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113 (2005) 843 [hep-th/0412141] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    T. Sakai and S. Sugimoto, More on a holographic dual of QCD, Prog. Theor. Phys. 114 (2005) 1083 [hep-th/0507073] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    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].
  35. [35]
    E.V. Gorbar, V.A. Miransky, I.A. Shovkovy and P.O. Sukhachov, Consistent hydrodynamic theory of chiral electrons in Weyl semimetals, Phys. Rev. B 97 (2018) 121105 [arXiv:1712.01289] [INSPIRE].
  36. [36]
    E.V. Gorbar, V.A. Miransky, I.A. Shovkovy and P.O. Sukhachov, Hydrodynamic electron flow in a Weyl semimetal slab: Role of Chern-Simons terms, Phys. Rev. B 97 (2018) 205119 [arXiv:1802.07265] [INSPIRE].
  37. [37]
    E.V. Gorbar, V.A. Miransky, I.A. Shovkovy and P.O. Sukhachov, Collective excitations in Weyl semimetals in the hydrodynamic regime, J. Phys. Condens. Matter 30 (2018) 275601 [arXiv:1802.10110] [INSPIRE].CrossRefGoogle Scholar
  38. [38]
    A.V. Sadofyev and M.V. Isachenkov, The Chiral magnetic effect in hydrodynamical approach, Phys. Lett. B 697 (2011) 404 [arXiv:1010.1550] [INSPIRE].
  39. [39]
    Y. Neiman and Y. Oz, Relativistic Hydrodynamics with General Anomalous Charges, JHEP 03 (2011) 023 [arXiv:1011.5107] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  40. [40]
    T. Kalaydzhyan and I. Kirsch, Fluid/gravity model for the chiral magnetic effect, Phys. Rev. Lett. 106 (2011) 211601 [arXiv:1102.4334] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    G.T. Horowitz, J.E. Santos and D. Tong, Optical Conductivity with Holographic Lattices, JHEP 07 (2012) 168 [arXiv:1204.0519] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  42. [42]
    M. Blake and D. Tong, Universal Resistivity from Holographic Massive Gravity, Phys. Rev. D 88 (2013) 106004 [arXiv:1308.4970] [INSPIRE].
  43. [43]
    R.A. Davison and B. Goutéraux, Dissecting holographic conductivities, JHEP 09 (2015) 090 [arXiv:1505.05092] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  44. [44]
    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].ADSCrossRefGoogle Scholar
  45. [45]
    Y. Bu, M. Lublinsky and A. Sharon, Anomalous transport from holography: Part I, JHEP 11 (2016) 093 [arXiv:1608.08595] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  46. [46]
    Y. Bu, M. Lublinsky and A. Sharon, Anomalous transport from holography: Part II, Eur. Phys. J. C 77 (2017) 194 [arXiv:1609.09054] [INSPIRE].
  47. [47]
    S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear Fluid Dynamics from Gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    S.A. Hartnoll, P.K. Kovtun, M. Muller and S. Sachdev, Theory of the Nernst effect near quantum phase transitions in condensed matter and in dyonic black holes, Phys. Rev. B 76 (2007) 144502 [arXiv:0706.3215] [INSPIRE].
  49. [49]
    S.A. Hartnoll, Theory of universal incoherent metallic transport, Nature Phys. 11 (2015) 54 [arXiv:1405.3651] [INSPIRE].ADSCrossRefGoogle Scholar
  50. [50]
    R.A. Davison, B. Goutéraux and S.A. Hartnoll, Incoherent transport in clean quantum critical metals, JHEP 10 (2015) 112 [arXiv:1507.07137] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  51. [51]
    B. Müller and D.-L. Yang, Viscous Leptons in the Quark Gluon Plasma, Phys. Rev. D 91 (2015) 125010 [arXiv:1503.06967] [INSPIRE].
  52. [52]
    J. Erlich, E. Katz, D.T. Son and M.A. Stephanov, QCD and a holographic model of hadrons, Phys. Rev. Lett. 95 (2005) 261602 [hep-ph/0501128] [INSPIRE].
  53. [53]
    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].ADSCrossRefGoogle Scholar
  54. [54]
    K. Landsteiner and Y. Liu, The holographic Weyl semi-metal, Phys. Lett. B 753 (2016) 453 [arXiv:1505.04772] [INSPIRE].ADSCrossRefGoogle Scholar
  55. [55]
    K. Landsteiner, Y. Liu and Y.-W. Sun, Quantum phase transition between a topological and a trivial semimetal from holography, Phys. Rev. Lett. 116 (2016) 081602 [arXiv:1511.05505] [INSPIRE].
  56. [56]
    K. Landsteiner, Y. Liu and Y.-W. Sun, Odd viscosity in the quantum critical region of a holographic Weyl semimetal, Phys. Rev. Lett. 117 (2016) 081604 [arXiv:1604.01346] [INSPIRE].
  57. [57]
    K. Landsteiner, Y. Liu and Y.-W. Sun, Negative magnetoresistivity in chiral fluids and holography, JHEP 03 (2015) 127 [arXiv:1410.6399] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  58. [58]
    Y.-W. Sun and Q. Yang, Negative magnetoresistivity in holography, JHEP 09 (2016) 122 [arXiv:1603.02624] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  59. [59]
    Y. Seo, G. Song, P. Kim, S. Sachdev and S.-J. Sin, Holography of the Dirac Fluid in Graphene with two currents, Phys. Rev. Lett. 118 (2017) 036601 [arXiv:1609.03582] [INSPIRE].
  60. [60]
    M. Rogatko and K.I. Wysokinski, Holographic calculation of the magneto-transport coefficients in Dirac semimetals, JHEP 01 (2018) 078 [arXiv:1712.01608] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  61. [61]
    M. Rogatko and K.I. Wysokinski, Two interacting current model of holographic Dirac fluid in graphene, Phys. Rev. D 97 (2018) 024053 [arXiv:1708.08051] [INSPIRE].
  62. [62]
    M. Ammon, M. Baggioli, A. Jiménez-Alba and S. Moeckel, A smeared quantum phase transition in disordered holography, JHEP 04 (2018) 068 [arXiv:1802.08650] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  63. [63]
    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].
  64. [64]
    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].
  65. [65]
    M. Blake, Momentum relaxation from the fluid/gravity correspondence, JHEP 09 (2015) 010 [arXiv:1505.06992] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  66. [66]
    M. Blake, Magnetotransport from the fluid/gravity correspondence, JHEP 10 (2015) 078 [arXiv:1507.04870] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  67. [67]
    M. Henningson and K. Skenderis, The Holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  68. [68]
    V. Balasubramanian and P. Kraus, A Stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  69. [69]
    M. Taylor, More on counterterms in the gravitational action and anomalies, hep-th/0002125 [INSPIRE].
  70. [70]
    S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [INSPIRE].ADSCrossRefGoogle Scholar
  71. [71]
    B. Sahoo and H.-U. Yee, Electrified plasma in AdS/CFT correspondence, JHEP 11 (2010) 095 [arXiv:1004.3541] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  72. [72]
    J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [INSPIRE].
  73. [73]
    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].
  74. [74]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  75. [75]
    S. Bhattacharyya, R. Loganayagam, I. Mandal, S. Minwalla and A. Sharma, Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions, JHEP 12 (2008) 116 [arXiv:0809.4272] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  76. [76]
    J. Hur, K.K. Kim and S.-J. Sin, Hydrodynamics with conserved current from the gravity dual, JHEP 03 (2009) 036 [arXiv:0809.4541] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  77. [77]
    G. Policastro, D.T. Son and A.O. Starinets, The Shear viscosity of strongly coupled N = 4 supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 87 (2001) 081601 [hep-th/0104066] [INSPIRE].
  78. [78]
    P. Kovtun, D.T. Son and A.O. Starinets, Viscosity in strongly interacting quantum field theories from black hole physics, Phys. Rev. Lett. 94 (2005) 111601 [hep-th/0405231] [INSPIRE].ADSCrossRefGoogle Scholar
  79. [79]
    D.T. Son and A.O. Starinets, Viscosity, Black Holes and Quantum Field Theory, Ann. Rev. Nucl. Part. Sci. 57 (2007) 95 [arXiv:0704.0240] [INSPIRE].ADSCrossRefGoogle Scholar
  80. [80]
    P.K. Kovtun and A.O. Starinets, Quasinormal modes and holography, Phys. Rev. D 72 (2005) 086009 [hep-th/0506184] [INSPIRE].
  81. [81]
    S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  82. [82]
    C.P. Herzog, Lectures on Holographic Superfluidity and Superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  83. [83]
    S.A. Hartnoll and C.P. Herzog, Ohm’s Law at strong coupling: S duality and the cyclotron resonance, Phys. Rev. D 76 (2007) 106012 [arXiv:0706.3228] [INSPIRE].
  84. [84]
    G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics. 2. Sound waves, JHEP 12 (2002) 054 [hep-th/0210220] [INSPIRE].
  85. [85]
    X.-H. Ge, Y. Matsuo, F.-W. Shu, S.-J. Sin and T. Tsukioka, Density Dependence of Transport Coefficients from Holographic Hydrodynamics, Prog. Theor. Phys. 120 (2008) 833 [arXiv:0806.4460] [INSPIRE].ADSCrossRefGoogle Scholar
  86. [86]
    E. Megias and F. Pena-Benitez, Holographic Gravitational Anomaly in First and Second Order Hydrodynamics, JHEP 05 (2013) 115 [arXiv:1304.5529] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Department of PhysicsHarbin Institute of TechnologyHarbinChina
  2. 2.CAS Key Laboratory of Theoretical Physics, Institute of Theoretical PhysicsChinese Academy of SciencesBeijingChina
  3. 3.School of Physical SciencesUniversity of Chinese Academy of SciencesBeijingChina
  4. 4.Department of AstronomyBeijing Normal UniversityBeijingChina
  5. 5.Asia Pacific Center for Theoretical Physics, APCTP HeadquartersPohangKorea
  6. 6.Center for Quantum Spacetime (CQUeST)Sogang UniversitySeoulKorea

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