Journal of High Energy Physics

, 2014:81 | Cite as

Thermoelectric DC conductivities from black hole horizons

  • Aristomenis Donos
  • Jerome P. Gauntlett
Open Access
Regular Article - Theoretical Physics


An analytic expression for the DC electrical conductivity in terms of black hole horizon data was recently obtained for a class of holographic black holes exhibiting momentum dissipation. We generalise this result to obtain analogous expressions for the DC thermoelectric and thermal conductivities. We illustrate our results using some holographic Q-lattice black holes as well as for some black holes with linear massless axions, in both D = 4 and D = 5 bulk spacetime dimensions, which include both spatially isotropic and anisotropic examples. We show that some recently constructed ground states of holographic Q-lattices, which can be either electrically insulating or metallic, are all thermal insulators.


Gauge-gravity correspondence Black Holes in String Theory AdS-CFT Correspondence Holography and condensed matter physics (AdS/CMT) 


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.


  1. [1]
    S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  2. [2]
    C.P. Herzog, Lectures on Holographic Superfluidity and Superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].Google Scholar
  3. [3]
    N. Iqbal and H. Liu, Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm, Phys. Rev. D 79 (2009) 025023 [arXiv:0809.3808] [INSPIRE].ADSGoogle Scholar
  4. [4]
    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].ADSCrossRefGoogle Scholar
  5. [5]
    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
  6. [6]
    A. Donos and J.P. Gauntlett, Novel metals and insulators from holography, JHEP 06 (2014) 007 [arXiv:1401.5077] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    B. Goutéraux, Charge transport in holography with momentum dissipation, JHEP 04 (2014) 181 [arXiv:1401.5436] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    T. Andrade and B. Withers, A simple holographic model of momentum relaxation, JHEP 05 (2014) 101 [arXiv:1311.5157] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    R.A. Davison, Momentum relaxation in holographic massive gravity, Phys. Rev. D 88 (2013) 086003 [arXiv:1306.5792] [INSPIRE].ADSGoogle Scholar
  10. [10]
    M. Blake and D. Tong, Universal Resistivity from Holographic Massive Gravity, Phys. Rev. D 88 (2013) 106004 [arXiv:1308.4970] [INSPIRE].ADSGoogle Scholar
  11. [11]
    R.A. Davison, K. Schalm and J. Zaanen, Holographic duality and the resistivity of strange metals, Phys. Rev. B 89 (2014) 245116 [arXiv:1311.2451] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    M. Blake, D. Tong and D. Vegh, Holographic Lattices Give the Graviton an Effective Mass, Phys. Rev. Lett. 112 (2014) 071602 [arXiv:1310.3832] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    M. Blake and A. Donos, Quantum Critical Transport and the Hall Angle, arXiv:1406.1659 [INSPIRE].
  14. [14]
    A. Donos and J.P. Gauntlett, Holographic Q-lattices, JHEP 04 (2014) 040 [arXiv:1311.3292] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    A. Donos and S.A. Hartnoll, Interaction-driven localization in holography, Nature Phys. 9 (2013) 649 [arXiv:1212.2998] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    N. Iizuka, S. Kachru, N. Kundu, P. Narayan, N. Sircar et al., Bianchi Attractors: A Classification of Extremal Black Brane Geometries, JHEP 07 (2012) 193 [arXiv:1201.4861] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  17. [17]
    A. Donos and J.P. Gauntlett, Helical superconducting black holes, Phys. Rev. Lett. 108 (2012) 211601 [arXiv:1203.0533] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    G.T. Horowitz, J.E. Santos and D. Tong, Optical Conductivity with Holographic Lattices, JHEP 07 (2012) 168 [arXiv:1204.0519] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  19. [19]
    G.T. Horowitz, J.E. Santos and D. Tong, Further Evidence for Lattice-Induced Scaling, JHEP 11 (2012) 102 [arXiv:1209.1098] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    G.T. Horowitz and J.E. Santos, General Relativity and the Cuprates, arXiv:1302.6586 [INSPIRE].
  21. [21]
    Y. Ling, C. Niu, J.-P. Wu and Z.-Y. Xian, Holographic Lattice in Einstein-Maxwell-Dilaton Gravity, JHEP 11 (2013) 006 [arXiv:1309.4580] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    P. Chesler, A. Lucas and S. Sachdev, Conformal field theories in a periodic potential: results from holography and field theory, Phys. Rev. D 89 (2014) 026005 [arXiv:1308.0329] [INSPIRE].ADSGoogle Scholar
  23. [23]
    A. Donos and J.P. Gauntlett, The thermoelectric properties of inhomogeneous holographic lattices, arXiv:1409.6875 [INSPIRE].
  24. [24]
    S.A. Hartnoll and D.M. Hofman, Locally Critical Resistivities from Umklapp Scattering, Phys. Rev. Lett. 108 (2012) 241601 [arXiv:1201.3917] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    R. Mahajan, M. Barkeshli and S.A. Hartnoll, Non-Fermi liquids and the Wiedemann-Franz law, Phys. Rev. B 88 (2013) 125107 [arXiv:1304.4249] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    T. Azeyanagi, W. Li and T. Takayanagi, On String Theory Duals of Lifshitz-like Fixed Points, JHEP 06 (2009) 084 [arXiv:0905.0688] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  27. [27]
    D. Mateos and D. Trancanelli, The anisotropic N = 4 super Yang-Mills plasma and its instabilities, Phys. Rev. Lett. 107 (2011) 101601 [arXiv:1105.3472] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    D. Mateos and D. Trancanelli, Thermodynamics and Instabilities of a Strongly Coupled Anisotropic Plasma, JHEP 07 (2011) 054 [arXiv:1106.1637] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    L. Cheng, X.-H. Ge and S.-J. Sin, Anisotropic plasma at finite U(1) chemical potential, JHEP 07 (2014) 083 [arXiv:1404.5027] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    V. Balasubramanian and P. Kraus, A Stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  31. [31]
    O. Gunnarsson, M. Calandra and J. Han, Colloquium: Saturation of electrical resistivity, Rev. Mod. Phys. 75 (2003) 1085 [cond-mat/0305412].ADSCrossRefGoogle Scholar
  32. [32]
    N. E. Hussey, K. Takenaka and H. Takagi, Universality of the Mott-Ioffe-Regel limit in metals, Phil. Mag. 84 (2004) 2847 [cond-mat/0404263].ADSCrossRefGoogle Scholar
  33. [33]
    Y. Bardoux, M.M. Caldarelli and C. Charmousis, Shaping black holes with free fields, JHEP 05 (2012) 054 [arXiv:1202.4458] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    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].ADSMathSciNetGoogle Scholar
  35. [35]
    E. Mefford and G.T. Horowitz, Simple holographic insulator, Phys. Rev. D 90 (2014) 084042 [arXiv:1406.4188] [INSPIRE].ADSGoogle Scholar
  36. [36]
    A. Amoretti, A. Braggio, N. Maggiore, N. Magnoli and D. Musso, Thermo-electric transport in gauge/gravity models with momentum dissipation, JHEP 09 (2014) 160 [arXiv:1406.4134] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.DAMTP, University of CambridgeCambridgeU.K.
  2. 2.Blackett LaboratoryImperial CollegeLondonU.K.

Personalised recommendations