Skip to main content

Quasinormal modes of charged magnetic black branes & chiral magnetic transport

A preprint version of the article is available at arXiv.

Abstract

We compute quasinormal modes (QNMs) of the metric and gauge field perturbations about black branes electrically and magnetically charged in the Einstein-Maxwell-Chern-Simons theory. By the gauge/gravity correspondence, this theory is dual to a particular class of field theories with a chiral anomaly, in a thermal charged plasma state subjected to a constant external magnetic field, B. The QNMs are dual to the poles of the two-point functions of the energy-momentum and axial current operators, and they encode information about the dissipation and transport of charges in the plasma. Complementary to the gravity calculation, we work out the hydrodynamic description of the dual field theory in the presence of a chiral anomaly, and a constant external B. We find good agreement with the weak field hydrodynamics, which can extend beyond the weak B regime into intermediate regimes. Furthermore, we provide results that can be tested against thermodynamics and hydrodynamics in the strong B regime. We find QNMs exhibiting Landau level behavior, which become long-lived at large B if the anomaly coefficient exceeds a critical magnitude. Chiral transport is analyzed beyond the hydrodynamic approximation for the five (formerly) hydrodynamic modes, including a chiral magnetic wave.

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]

    K. Fukushima, D.E. Kharzeev and H.J. Warringa, The Chiral Magnetic Effect, Phys. Rev. D 78 (2008) 074033 [arXiv:0808.3382] [INSPIRE].

    ADS  Google Scholar 

  3. [3]

    D.T. Son and P. Surowka, Hydrodynamics with Triangle Anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  4. [4]

    J. Erdmenger, M. Haack, M. Kaminski and A. Yarom, Fluid dynamics of R-charged black holes, JHEP 01 (2009) 055 [arXiv:0809.2488] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  5. [5]

    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].

    ADS  Article  MATH  Google Scholar 

  6. [6]

    A. Vilenkin, Parity Nonconservation and Rotating Black Holes, Phys. Rev. Lett. 41 (1978) 1575 [INSPIRE].

    ADS  Article  Google Scholar 

  7. [7]

    A. Vilenkin, Equilibrium parity violating current in a magnetic field, Phys. Rev. D 22 (1980) 3080 [INSPIRE].

    ADS  Google Scholar 

  8. [8]

    K. Jensen, P. Kovtun and A. Ritz, Chiral conductivities and effective field theory, JHEP 10 (2013) 186 [arXiv:1307.3234] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  9. [9]

    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].

    ADS  Article  Google Scholar 

  10. [10]

    Q. Li et al., Observation of the chiral magnetic effect in ZrTe5, Nature Phys. 12 (2016) 550 [arXiv:1412.6543] [INSPIRE].

    ADS  Article  Google Scholar 

  11. [11]

    F. Arnold et al., Negative magnetoresistance without well-defined chirality in the Weyl semimetal TaP, Nature Commun. 7 (2016) 1615 [arXiv:1506.06577] [INSPIRE].

    Article  Google Scholar 

  12. [12]

    C. Zhang et al., Detection of chiral anomaly and valley transport in Dirac semimetals, arXiv:1504.07698 [INSPIRE].

  13. [13]

    Z. Wang et al., Helicity protected ultrahigh mobility Weyl fermions in NbP, Phys. Rev. B 93 (2016) 121112 [arXiv:1506.00924] [INSPIRE].

    ADS  Article  Google Scholar 

  14. [14]

    X. Yang, Y. Liu, Z. Wang, Y. Zheng and Z.-a. Xu, Chiral anomaly induced negative magnetoresistance in topological Weyl semimetal NbAs, arXiv:1506.03190 [INSPIRE].

  15. [15]

    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].

    ADS  Article  Google Scholar 

  16. [16]

    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].

  17. [17]

    STAR collaboration, B.I. Abelev et al., Azimuthal Charged-Particle Correlations and Possible Local Strong Parity Violation, Phys. Rev. Lett. 103 (2009) 251601 [arXiv:0909.1739] [INSPIRE].

  18. [18]

    STAR collaboration, B.I. Abelev et al., Observation of charge-dependent azimuthal correlations and possible local strong parity violation in heavy ion collisions, Phys. Rev. C 81 (2010) 054908 [arXiv:0909.1717] [INSPIRE].

  19. [19]

    STAR collaboration, L. Adamczyk et al., Measurement of charge multiplicity asymmetry correlations in high-energy nucleus-nucleus collisions at \( \sqrt{s_{\;N\;N}} \) = 200 GeV, Phys. Rev. C 89 (2014) 044908 [arXiv:1303.0901] [INSPIRE].

  20. [20]

    STAR collaboration, L. Adamczyk et al., Beam-energy dependence of charge separation along the magnetic field in Au+Au collisions at RHIC, Phys. Rev. Lett. 113 (2014) 052302 [arXiv:1404.1433] [INSPIRE].

  21. [21]

    STAR collaboration, L. Adamczyk et al., Fluctuations of charge separation perpendicular to the event plane and local parity violation in \( \sqrt{s_{\;N\;N}} \) = 200 GeV Au+Au collisions at the BNL Relativistic Heavy Ion Collider, Phys. Rev. C 88 (2013) 064911 [arXiv:1302.3802] [INSPIRE].

  22. [22]

    ALICE collaboration, Charge separation relative to the reaction plane in Pb-Pb collisions at \( \sqrt{s_{\;N\;N}} \) = 2.76 TeV, Phys. Rev. Lett. 110 (2013) 012301 [arXiv:1207.0900] [INSPIRE].

  23. [23]

    F. Wang, Effects of Cluster Particle Correlations on Local Parity Violation Observables, Phys. Rev. C 81 (2010) 064902 [arXiv:0911.1482] [INSPIRE].

    ADS  Google Scholar 

  24. [24]

    A. Bzdak, V. Koch and J. Liao, Azimuthal correlations from transverse momentum conservation and possible local parity violation, Phys. Rev. C 83 (2011) 014905 [arXiv:1008.4919] [INSPIRE].

    ADS  Google Scholar 

  25. [25]

    S. Schlichting and S. Pratt, Charge conservation at energies available at the BNL Relativistic Heavy Ion Collider and contributions to local parity violation observables, Phys. Rev. C 83 (2011) 014913 [arXiv:1009.4283] [INSPIRE].

  26. [26]

    N. Abbasi, A. Davody, K. Hejazi and Z. Rezaei, Hydrodynamic Waves in an Anomalous Charged Fluid, Phys. Lett. B 762 (2016) 23 [arXiv:1509.08878] [INSPIRE].

    ADS  Article  Google Scholar 

  27. [27]

    T. Kalaydzhyan and E. Murchikova, Thermal chiral vortical and magnetic waves: new excitation modes in chiral fluids, Nucl. Phys. B 919 (2017) 173 [arXiv:1609.00024] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  28. [28]

    N. Abbasi, D. Allahbakhshi, A. Davody and S.F. Taghavi, Collective Excitations in QCD Plasma, arXiv:1612.08614 [INSPIRE].

  29. [29]

    X.-G. Huang, A. Sedrakian and D.H. Rischke, Kubo formulae for relativistic fluids in strong magnetic fields, Annals Phys. 326 (2011) 3075 [arXiv:1108.0602] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  30. [30]

    P. Kovtun, Thermodynamics of polarized relativistic matter, JHEP 07 (2016) 028 [arXiv:1606.01226] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  31. [31]

    W. Israel, The Dynamics of Polarization, Gen. Rel. Grav. 9 (1978) 451 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  32. [32]

    D.E. Kharzeev and H.-U. Yee, Chiral Magnetic Wave, Phys. Rev. D 83 (2011) 085007 [arXiv:1012.6026] [INSPIRE].

    ADS  Google Scholar 

  33. [33]

    J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].

    MathSciNet  Article  MATH  Google Scholar 

  34. [34]

    M. Ammon and J. Erdmenger, Gauge/gravity duality, Cambridge University Press, Cambridge, U.K. (2015).

    Book  MATH  Google Scholar 

  35. [35]

    H. Nastase, Introduction to the AdS/CFT Correspondence, Cambridge University Press, Cambridge, U.K. (2015).

    Book  Google Scholar 

  36. [36]

    J. Zaanen, Y. Liu, Y.-W. Sun and K. Schalm, Holographic Duality in Condensed Matter Physics, Cambridge University Press, Cambridge, U.K. (2016).

    Google Scholar 

  37. [37]

    U.W. Heinz, The Strongly coupled quark-gluon plasma created at RHIC, J. Phys. A 42 (2009) 214003 [arXiv:0810.5529] [INSPIRE].

    ADS  Google Scholar 

  38. [38]

    K. Landsteiner and Y. Liu, The holographic Weyl semi-metal, Phys. Lett. B 753 (2016) 453 [arXiv:1505.04772] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  39. [39]

    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].

    ADS  Article  Google Scholar 

  40. [40]

    C. Copetti, J. Fernández-Pendás and K. Landsteiner, Axial Hall effect and universality of holographic Weyl semi-metals, JHEP 02 (2017) 138 [arXiv:1611.08125] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  41. [41]

    M. Ammon, M. Heinrich, A. Jiménez-Alba and S. Moeckel, Surface States in Holographic Weyl Semimetals, arXiv:1612.00836 [INSPIRE].

  42. [42]

    G. Grignani, A. Marini, F. Pena-Benitez and S. Speziali, AC conductivity for a holographic Weyl Semimetal, JHEP 03 (2017) 125 [arXiv:1612.00486] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  43. [43]

    D. Kharzeev, Y. Kikuchi and R. Meyer, Chiral magnetic effect without chirality source in asymmetric Weyl semimetals, arXiv:1610.08986 [INSPIRE].

  44. [44]

    E. Berti, V. Cardoso and A.O. Starinets, Quasinormal modes of black holes and black branes, Class. Quant. Grav. 26 (2009) 163001 [arXiv:0905.2975] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  45. [45]

    R.A. Konoplya and A. Zhidenko, Quasinormal modes of black holes: From astrophysics to string theory, Rev. Mod. Phys. 83 (2011) 793 [arXiv:1102.4014] [INSPIRE].

    ADS  Article  Google 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].

    ADS  Article  Google Scholar 

  47. [47]

    Y. Bu, M. Lublinsky and A. Sharon, Anomalous transport from holography: Part I, JHEP 11 (2016) 093 [arXiv:1608.08595] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  48. [48]

    M.P. Heller, D. Mateos, W. van der Schee and M. Triana, Holographic isotropization linearized, JHEP 09 (2013) 026 [arXiv:1304.5172] [INSPIRE].

    ADS  Article  Google Scholar 

  49. [49]

    A. Buchel, M.P. Heller and R.C. Myers, Equilibration rates in a strongly coupled nonconformal quark-gluon plasma, Phys. Rev. Lett. 114 (2015) 251601 [arXiv:1503.07114] [INSPIRE].

    ADS  Article  Google Scholar 

  50. [50]

    J.F. Fuini and L.G. Yaffe, Far-from-equilibrium dynamics of a strongly coupled non-Abelian plasma with non-zero charge density or external magnetic field, JHEP 07 (2015) 116 [arXiv:1503.07148] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  51. [51]

    S. Janiszewski and M. Kaminski, Quasinormal modes of magnetic and electric black branes versus far from equilibrium anisotropic fluids, Phys. Rev. D 93 (2016) 025006 [arXiv:1508.06993] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  52. [52]

    R.A. Janik, J. Jankowski and H. Soltanpanahi, Quasinormal modes and the phase structure of strongly coupled matter, JHEP 06 (2016) 047 [arXiv:1603.05950] [INSPIRE].

    ADS  Article  Google Scholar 

  53. [53]

    M. Attems et al., Thermodynamics, transport and relaxation in non-conformal theories, JHEP 10 (2016) 155 [arXiv:1603.01254] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  54. [54]

    D.T. Son and A.O. Starinets, Minkowski space correlators in AdS/CFT correspondence: Recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  55. [55]

    P.K. Kovtun and A.O. Starinets, Quasinormal modes and holography, Phys. Rev. D 72 (2005) 086009 [hep-th/0506184] [INSPIRE].

    ADS  Google Scholar 

  56. [56]

    A. Núñez and A.O. Starinets, AdS/CFT correspondence, quasinormal modes and thermal correlators in N = 4 SYM, Phys. Rev. D 67 (2003) 124013 [hep-th/0302026] [INSPIRE].

    ADS  Google Scholar 

  57. [57]

    B. Sahoo and H.-U. Yee, Holographic chiral shear waves from anomaly, Phys. Lett. B 689 (2010) 206 [arXiv:0910.5915] [INSPIRE].

    ADS  Article  Google Scholar 

  58. [58]

    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].

    ADS  Article  MATH  Google Scholar 

  59. [59]

    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].

    ADS  MathSciNet  Article  Google Scholar 

  60. [60]

    Y. Matsuo, S.-J. Sin, S. Takeuchi, T. Tsukioka and C.-M. Yoo, Sound Modes in Holographic Hydrodynamics for Charged AdS Black Hole, Nucl. Phys. B 820 (2009) 593 [arXiv:0901.0610] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  61. [61]

    E. D’Hoker and P. Kraus, Charged Magnetic Brane Solutions in AdS 5 and the fate of the third law of thermodynamics, JHEP 03 (2010) 095 [arXiv:0911.4518] [INSPIRE].

    Article  MATH  Google Scholar 

  62. [62]

    A. Buchel and J.T. Liu, Gauged supergravity from type IIB string theory on Y p,q manifolds, Nucl. Phys. B 771 (2007) 93 [hep-th/0608002] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  63. [63]

    J.P. Gauntlett, E. Ó. Colgáin and O. Varela, Properties of some conformal field theories with M-theory duals, JHEP 02 (2007) 049 [hep-th/0611219] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  64. [64]

    J.P. Gauntlett and O. Varela, Consistent Kaluza-Klein reductions for general supersymmetric AdS solutions, Phys. Rev. D 76 (2007) 126007 [arXiv:0707.2315] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  65. [65]

    E. Ó. Colgáin, M.M. Sheikh-Jabbari, J.F. Vázquez-Poritz, H. Yavartanoo and Z. Zhang, Warped Ricci-flat reductions, Phys. Rev. D 90 (2014) 045013 [arXiv:1406.6354] [INSPIRE].

    ADS  Google Scholar 

  66. [66]

    S.I. Finazzo, R. Critelli, R. Rougemont and J. Noronha, Momentum transport in strongly coupled anisotropic plasmas in the presence of strong magnetic fields, Phys. Rev. D 94 (2016) 054020 [arXiv:1605.06061] [INSPIRE].

    ADS  Google Scholar 

  67. [67]

    R. Critelli, S.I. Finazzo, M. Zaniboni and J. Noronha, Anisotropic shear viscosity of a strongly coupled non-Abelian plasma from magnetic branes, Phys. Rev. D 90 (2014) 066006 [arXiv:1406.6019] [INSPIRE].

    ADS  Google Scholar 

  68. [68]

    M. Ammon, J. Leiber and R.P. Macedo, Phase diagram of 4D field theories with chiral anomaly from holography, JHEP 03 (2016) 164 [arXiv:1601.02125] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  69. [69]

    S.L. Adler, Axial vector vertex in spinor electrodynamics, Phys. Rev. 177 (1969) 2426 [INSPIRE].

    ADS  Article  Google Scholar 

  70. [70]

    J.S. Bell and R. Jackiw, A PCAC puzzle: π 0γγ in the σ-model, Nuovo Cim. A 60 (1969) 47 [INSPIRE].

    ADS  Article  Google Scholar 

  71. [71]

    E. D’Hoker and P. Kraus, Magnetic Brane Solutions in AdS, JHEP 10 (2009) 088 [arXiv:0908.3875] [INSPIRE].

    MathSciNet  Article  Google Scholar 

  72. [72]

    M. Henningson and K. Skenderis, The Holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  73. [73]

    V. Balasubramanian and P. Kraus, A stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  74. [74]

    M. Taylor, More on counterterms in the gravitational action and anomalies, hep-th/0002125 [INSPIRE].

  75. [75]

    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  76. [76]

    A. Bilal and C.-S. Chu, A note on the chiral anomaly in the AdS/CFT correspondence and 1/N 2 correction, Nucl. Phys. B 562 (1999) 181 [hep-th/9907106] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  77. [77]

    K. Jensen, R. Loganayagam and A. Yarom, Anomaly inflow and thermal equilibrium, JHEP 05 (2014) 134 [arXiv:1310.7024] [INSPIRE].

    ADS  Article  Google Scholar 

  78. [78]

    K. Jensen, M. Kaminski, P. Kovtun, R. Meyer, A. Ritz and A. Yarom, Parity-Violating Hydrodynamics in 2+1 Dimensions, JHEP 05 (2012) 102 [arXiv:1112.4498] [INSPIRE].

    ADS  Article  Google Scholar 

  79. [79]

    K. Jensen, M. Kaminski, P. Kovtun, R. Meyer, A. Ritz and A. Yarom, Towards hydrodynamics without an entropy current, Phys. Rev. Lett. 109 (2012) 101601 [arXiv:1203.3556] [INSPIRE].

    ADS  Article  Google Scholar 

  80. [80]

    K. Landsteiner, E. Megias and F. Pena-Benitez, Gravitational Anomaly and Transport, Phys. Rev. Lett. 107 (2011) 021601 [arXiv:1103.5006] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  81. [81]

    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].

    ADS  Article  MATH  Google Scholar 

  82. [82]

    K. Landsteiner, E. Megias, L. Melgar and F. Pena-Benitez, Holographic Gravitational Anomaly and Chiral Vortical Effect, JHEP 09 (2011) 121 [arXiv:1107.0368] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  83. [83]

    I. Amado, K. Landsteiner and F. Pena-Benitez, Anomalous transport coefficients from Kubo formulas in Holography, JHEP 05 (2011) 081 [arXiv:1102.4577] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  84. [84]

    M. Ammon, S. Grieninger, A. Jimenez-Alba, R.P. Macedo and L. Melgar, Holographic quenches and anomalous transport, JHEP 09 (2016) 131 [arXiv:1607.06817] [INSPIRE].

    ADS  Article  Google Scholar 

  85. [85]

    M. Edalati, J.I. Jottar and R.G. Leigh, Shear Modes, Criticality and Extremal Black Holes, JHEP 04 (2010) 075 [arXiv:1001.0779] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  86. [86]

    M. Edalati, J.I. Jottar and R.G. Leigh, Holography and the sound of criticality, JHEP 10 (2010) 058 [arXiv:1005.4075] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  87. [87]

    A. Jimenez-Alba and L. Melgar, Anomalous Transport in Holographic Chiral Superfluids via Kubo Formulae, JHEP 10 (2014) 120 [arXiv:1404.2434] [INSPIRE].

    ADS  Article  Google Scholar 

  88. [88]

    Y. Liu and F. Pena-Benitez, Spatially modulated instabilities of holographic gauge-gravitational anomaly, arXiv:1612.00470 [INSPIRE].

  89. [89]

    S. Grozdanov, D.M. Hofman and N. Iqbal, Generalized global symmetries and dissipative magnetohydrodynamics, arXiv:1610.07392 [INSPIRE].

  90. [90]

    M. Rangamani, Gravity and Hydrodynamics: Lectures on the fluid-gravity correspondence, Class. Quant. Grav. 26 (2009) 224003 [arXiv:0905.4352] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  91. [91]

    P. Kovtun, Lectures on hydrodynamic fluctuations in relativistic theories, J. Phys. A 45 (2012) 473001 [arXiv:1205.5040] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  92. [92]

    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].

    ADS  Google Scholar 

  93. [93]

    A.O. Starinets, Quasinormal modes of near extremal black branes, Phys. Rev. D 66 (2002) 124013 [hep-th/0207133] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  94. [94]

    S. Janiszewski, Perturbations of Moving Membranes in AdS 7, JHEP 09 (2012) 093 [arXiv:1112.0085] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  95. [95]

    S. Nakamura, H. Ooguri and C.-S. Park, Gravity Dual of Spatially Modulated Phase, Phys. Rev. D 81 (2010) 044018 [arXiv:0911.0679] [INSPIRE].

    ADS  Google Scholar 

  96. [96]

    A. Donos and J.P. Gauntlett, Black holes dual to helical current phases, Phys. Rev. D 86 (2012) 064010 [arXiv:1204.1734] [INSPIRE].

    ADS  Google Scholar 

Download references

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.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Matthias Kaminski.

Additional information

ArXiv ePrint: 1701.05565

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ammon, M., Kaminski, M., Koirala, R. et al. Quasinormal modes of charged magnetic black branes & chiral magnetic transport. J. High Energ. Phys. 2017, 67 (2017). https://doi.org/10.1007/JHEP04(2017)067

Download citation

Keywords

  • AdS-CFT Correspondence
  • Gauge-gravity correspondence
  • Holography and condensed matter physics (AdS/CMT)
  • Quark-Gluon Plasma