Magneto-transport in an anomalous fluid with weakly broken symmetries, in weak and strong regime

  • Navid AbbasiEmail author
  • Armin Ghazi
  • Farid Taghinavaz
  • Omid Tavakol
Open Access
Regular Article - Theoretical Physics


We consider a fluid with weakly broken time and translation symmetries. We assume the fluid also possesses a U(1) symmetry which is not only weakly broken, but is anomalous. We use the second order chiral quasi-hydrodynamics to compute the magneto conductivities of this fluid in the presence of a weak magnetic field. Analogous to the electrical and thermoelectric conductivities, it turns out that the thermal conductivity depends on the coefficient of mixed gauge-gravitational anomaly. Our results can be applied to the hydrodynamic regime of every arbitrary system, once the thermodynamics of that system is known. By applying them to a free system of Weyl fermions at low temperature limit Tμ, we find that our fluid is Onsager reciprocal if the relaxation in all energy, momentum and charge channels occurs at the same rate. In the high temperature limit Tμ, we consider a strongly coupled SU(Nc) gauge theory with Nc ≫ 1. Its holographic dual in thermal equilibrium is a magnetized charged brane from which, we compute the thermodynamic quantities and subsequently evaluate the conductivities in gauge theory. On the way, we show that analogous to the weak regime in the system of Weyl fermions, an energy cutoff emerges to regulate the thermodynamic quantities in the strong regime of boundary gauge theory. From this gravity background we also find the coefficients of chiral magnetic effect in agreement with the well-known result of Son-Surowka.


AdS-CFT Correspondence Holography and quark-gluon plasmas 


Open Access

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  1. [1]
    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
  2. [2]
    D.T. Son and P. Surowka, Hydrodynamics with triangle anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    K. Landsteiner, Notes on anomaly induced transport, Acta Phys. Polon. B 47 (2016) 2617 [arXiv:1610.04413] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    K. Landsteiner, E. Megias and F. Pena-Benitez, Anomalous transport from kubo formulae, Lect. Notes Phys. 871 (2013) 433 [arXiv:1207.5808] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    N. Banerjee et al., Hydrodynamics from charged black branes, JHEP 01 (2011) 094 [arXiv:0809.2596] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  6. [6]
    J. Erdmenger, M. Haack, M. Kaminski and A. Yarom, Fluid dynamics of R-charged black holes, JHEP 01 (2009) 055 [arXiv:0809.2488] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    K. Landsteiner, E. Megias and F. Pena-Benitez, Gravitational anomaly and transport, Phys. Rev. Lett. 107 (2011) 021601 [arXiv:1103.5006] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  8. [8]
    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].ADSCrossRefzbMATHGoogle Scholar
  9. [9]
    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].ADSCrossRefzbMATHGoogle Scholar
  10. [10]
    N. Yamamoto, Chiral Alfvén wave in anomalous hydrodynamics, Phys. Rev. Lett. 115 (2015) 141601 [arXiv:1505.05444] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    M.N. Chernodub, Chiral heat wave and mixing of magnetic, vortical and heat waves in chiral media, JHEP 01 (2016) 100 [arXiv:1509.01245] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    M.N. Chernodub, A. Cortijo and K. Landsteiner, Zilch vortical effect, Phys. Rev. D 98 (2018) 065016 [arXiv:1807.10705] [INSPIRE].ADSGoogle Scholar
  13. [13]
    D.E. Kharzeev and H.-U. Yee, Chiral magnetic wave, Phys. Rev. D 83 (2011) 085007 [arXiv:1012.6026] [INSPIRE].ADSGoogle Scholar
  14. [14]
    K. Jensen, R. Loganayagam and A. Yarom, Thermodynamics, gravitational anomalies and cones, JHEP 02 (2013) 088 [arXiv:1207.5824] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    H.B. Nielsen and M. Ninomiya, Adler-Bell-Jackiw anomaly and Weyl fermions in crystal, Phys. Lett. 130B (1983) 389 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  16. [16]
    D.T. Son and B.Z. Spivak, Chiral anomaly and classical negative magnetoresistance of Weyl metals, Phys. Rev. B 88 (2013) 104412 [arXiv:1206.1627] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    E.V. Gorbar, V.A. Miransky and I.A. Shovkovy, Chiral anomaly, dimensional reduction and magnetoresistivity of Weyl and Dirac semimetals, Phys. Rev. B 89 (2014) 085126 [arXiv:1312.0027] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    Q. Li et al., Observation of the chiral magnetic effect in ZrTe 5, Nature Phys. 12 (2016) 550 [arXiv:1412.6543] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    J. Gooth et al., Experimental signatures of the mixed axial-gravitational anomaly in the Weyl semimetal NbP, Nature 547 (2017) 324 [arXiv:1703.10682] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    K. Landsteiner, Y. Liu and Y.-W. Sun, Negative magnetoresistivity in chiral fluids and holography, JHEP 03 (2015) 127 [arXiv:1410.6399] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    S. Grozdanov, A. Lucas and N. Poovuttikul, Holography and hydrodynamics with weakly broken symmetries, Phys. Rev. D 99 (2019) 086012 [arXiv:1810.10016] [INSPIRE].ADSGoogle Scholar
  22. [22]
    S. Grozdanov and N. Poovuttikul, Generalised global symmetries in holography: magnetohydrodynamic waves in a strongly interacting plasma, JHEP 04 (2019) 141 [arXiv:1707.04182] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    A. Lucas and K.C. Fong, Hydrodynamics of electrons in graphene, J. Phys. Condens. Matter 30 (2018) 053001 [arXiv:1710.08425] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    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].ADSCrossRefGoogle Scholar
  25. [25]
    J.-H. Gao et al., Chiral anomaly and local polarization effect from quantum kinetic approach, Phys. Rev. Lett. 109 (2012) 232301 [arXiv:1203.0725] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    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
  27. [27]
    Y. Hidaka, S. Pu and D.-L. Yang, Relativistic chiral kinetic theory from quantum field theories, Phys. Rev. D 95 (2017) 091901 [arXiv:1612.04630] [INSPIRE].ADSGoogle Scholar
  28. [28]
    J.-Y. Chen, D.T. Son and M.A. Stephanov, Collisions in chiral kinetic theory, Phys. Rev. Lett. 115 (2015) 021601 [arXiv:1502.06966] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    J.-Y. Chen, D.T. Son, M.A. Stephanov, H.-U. Yee and Y. Yin, Lorentz Invariance in Chiral Kinetic Theory, Phys. Rev. Lett. 113 (2014) 182302 [arXiv:1404.5963] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    M.A. Stephanov and Y. Yin, Chiral kinetic theory, Phys. Rev. Lett. 109 (2012) 162001 [arXiv:1207.0747] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    N. Abbasi, F. Taghinavaz and K. Naderi, Hydrodynamic excitations from chiral kinetic theory and the hydrodynamic frames, JHEP 03 (2018) 191 [arXiv:1712.06175] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    N. Abbasi, F. Taghinavaz and O. Tavakol, Magneto-transport in a chiral fluid from kinetic theory, JHEP 03 (2019) 051 [arXiv:1811.05532] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  33. [33]
    N. Abbasi and A. Ghazi, work in progress.Google Scholar
  34. [34]
    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].
  35. [35]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  36. [36]
    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].CrossRefzbMATHGoogle Scholar
  37. [37]
    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
  38. [38]
    S. Grozdanov, D.M. Hofman and N. Iqbal, Generalized global symmetries and dissipative magnetohydrodynamics, Phys. Rev. D 95 (2017) 096003 [arXiv:1610.07392] [INSPIRE].ADSGoogle Scholar
  39. [39]
    J. Hernandez and P. Kovtun, Relativistic magnetohydrodynamics, JHEP 05 (2017) 001 [arXiv:1703.08757] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  40. [40]
    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].ADSCrossRefGoogle Scholar
  41. [41]
    G.D. Moore and K.A. Sohrabi, Thermodynamical second-order hydrodynamic coefficients, JHEP 11 (2012) 148 [arXiv:1210.3340] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  43. [43]
    C.P. Herzog, Lectures on holographic superfluidity and superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  44. [44]
    S.A. Hartnoll, A. Lucas and S. Sachdev, Holographic quantum matter, arXiv:1612.07324 [INSPIRE].
  45. [45]
    E. Shuryak, Why does the quark gluon plasma at RHIC behave as a nearly ideal fluid?, Prog. Part. Nucl. Phys. 53 (2004) 273 [hep-ph/0312227] [INSPIRE].
  46. [46]
    V. Balasubramanian and P. Kraus, A stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  47. [47]
    W. Li, S. Lin and J. Mei, Conductivities of magnetic quark-gluon plasma at strong coupling, Phys. Rev. D 98 (2018) 114014 [arXiv:1809.02178] [INSPIRE].ADSGoogle Scholar
  48. [48]
    A. Lucas, R.A. Davison and S. Sachdev, Hydrodynamic theory of thermoelectric transport and negative magnetoresistance in Weyl semimetals, Proc. Nat. Acad. Sci. 113 (2016) 9463 [arXiv:1604.08598] [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    R.A. Davison et al., Thermoelectric transport in disordered metals without quasiparticles: The Sachdev-Ye-Kitaev models and holography, Phys. Rev. B 95 (2017) 155131 [arXiv:1612.00849] [INSPIRE].ADSCrossRefGoogle Scholar
  50. [50]
    A. Donos and J.P. Gauntlett, Thermoelectric DC conductivities from black hole horizons, JHEP 11 (2014) 081 [arXiv:1406.4742] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    A. Mokhtari, S.A. Hosseini Mansoori and K. Bitaghsir Fadafan, Diffusivities bounds in the presence of Weyl corrections, Phys. Lett. B 785 (2018) 591 [arXiv:1710.03738] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  52. [52]
    N. Abbasi, F. Taghinavaz and O. Tavakol, work in progress.Google Scholar
  53. [53]
    M. Stephanov and Y. Yin, Hydrodynamics with parametric slowing down and fluctuations near the critical point, Phys. Rev. D 98 (2018) 036006 [arXiv:1712.10305] [INSPIRE].ADSMathSciNetGoogle Scholar
  54. [54]
    D. Roychowdhury, Magnetoconductivity in chiral Lifshitz hydrodynamics, JHEP 09 (2015) 145 [arXiv:1508.02002] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  55. [55]
    Y.-W. Sun and Q. Yang, Negative magnetoresistivity in holography, JHEP 09 (2016) 122 [arXiv:1603.02624] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  56. [56]
    M. Rogatko and K.I. Wysokinski, Magnetotransport of Weyl semimetals with2 topological charge and chiral anomaly, JHEP 01 (2019) 049 [arXiv:1810.07521] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  57. [57]
    M. Rogatko and K.I. Wysokinski, Hydrodynamics of topological Dirac semi-metals with chiral anD2 anomalies, JHEP 09 (2018) 136 [arXiv:1804.02202] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  58. [58]
    K. Jensen et al., Towards hydrodynamics without an entropy current, Phys. Rev. Lett. 109 (2012) 101601 [arXiv:1203.3556] [INSPIRE].ADSCrossRefGoogle Scholar
  59. [59]
    N. Banerjee et al., Constraints on fluid dynamics from equilibrium partition functions, JHEP 09 (2012) 046 [arXiv:1203.3544] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  60. [60]
    P. Kovtun, Lectures on hydrodynamic fluctuations in relativistic theories, J. Phys. A 45 (2012) 473001 [arXiv:1205.5040] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  61. [61]
    L.D. Lanadau and E. Lifshitz, Statistical physics, Course on Theoretical Physics volume 5, Butterworth-Heinemann, U.K. (1980).Google Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Navid Abbasi
    • 1
    Email author
  • Armin Ghazi
    • 2
  • Farid Taghinavaz
    • 1
  • Omid Tavakol
    • 2
  1. 1.School of Particles and AcceleratorsInstitute for Research in Fundamental Sciences (IPM)TehranIran
  2. 2.Department of PhysicsSharif University of TechnologyTehranIran

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