Strange metals at finite ’t Hooft coupling

Regular Article - Theoretical Physics


In this paper, we consider the AdS–Schwarzschild black hole in light-cone coordinates which exhibits non-relativistic z=2 Schrodinger symmetry. Then, we use the AdS/CFT correspondence to investigate the effect of finite-coupling corrections to two important properties of the strange metals which are the Ohmic resistivity and the inverse Hall angle. It is shown that the Ohmic resistivity and inverse Hall angle are linearly and quadratically temperature dependent in the case of \(\mathcal{R}^{4}\) corrections, respectively, while in the case of Gauss–Bonnet gravity, we find that the inverse Hall angle is quadratically temperature dependent and the Ohmic conductivity can never be linearly temperature dependent.


Black Hole Gauge Field Black Brane Hooft Coupling Hall Conductivity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



It is a pleasure to thank M. Ali-Akbari, M. Alishahiha and M. Sheikh-Jabbari for very useful discussions and especially thank Bom Soo Kim for reading the manuscript and useful comments. Also we are very grateful to and thank M. Sohani for carefully reading the draft. We would like to thank the referee of EPJC for giving constructive comments which helped improving the paper. This research was supported by Shahrood University of Technology.


  1. 1.
    S.A. Hartnoll, Lectures on holographic methods for condensed matter physics. Class. Quantum Gravity 26, 224002 (2009). arXiv:0903.3246 MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    J. McGreevy, Holographic duality with a view toward many-body physics. Adv. High Energy Phys. 2010, 723105 (2010). arXiv:0909.0518 Google Scholar
  3. 3.
    S.A. Hartnoll, Horizons, holography and condensed matter. arXiv:1106.4324
  4. 4.
    N. Iqbal, H. Liu, M. Mezei, Lectures on holographic non-Fermi liquids and quantum phase transitions. arXiv:1110.3814
  5. 5.
    G.R. Stewart, Non-Fermi-liquid behavior in d- and f-electron metals. Rev. Mod. Phys. 73, 797 (2001) [Addendum: Rev. Mod. Phys. 78, 743 (2006)] ADSCrossRefGoogle Scholar
  6. 6.
    R.A. Cooper, Y. Wang, B. Vignolle, O.J. Lipscombe, S.M. Hayden, Y. Tanabe, T. Adachi, Y. Koike, M. Nohara, H. Takagi, C. Proust, N.E. Hussey, Anomalous criticality in the electrical resistivity of La2−xSrxCuO4. Science 323, 603 (2009) ADSCrossRefGoogle Scholar
  7. 7.
    S. Sachdev, Strange metals and the AdS/CFT correspondence. J. Stat. Mech. 1011, P11022 (2010). arXiv:1010.0682 [cond-mat.str-el] CrossRefGoogle Scholar
  8. 8.
    D.T. Son, Toward an AdS/cold atoms correspondence: a geometric realization of the Schrodinger symmetry. Phys. Rev. D 78, 046003 (2008). arXiv:0804.3972 [hep-th] MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    K. Balasubramanian, J. McGreevy, Gravity duals for non-relativistic CFTs. Phys. Rev. Lett. 101, 061601 (2008). arXiv:0804.4053 [hep-th] MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    J. Maldacena, D. Martelli, Y. Tachikawa, Comments on string theory backgrounds with non-relativistic conformal symmetry. J. High Energy Phys. 0810, 072 (2008). arXiv:0807.1100 [hep-th] MathSciNetADSCrossRefGoogle Scholar
  11. 11.
    M. Alishahiha, O.J. Ganor, Twisted backgrounds, PP waves and nonlocal field theories. J. High Energy Phys. 0303, 006 (2003). arXiv:hep-th/0301080 MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    W.D. Goldberger, AdS/CFT duality for non-relativistic field theory. J. High Energy Phys. 0903, 069 (2009). arXiv:0806.2867 [hep-th] MathSciNetADSCrossRefGoogle Scholar
  13. 13.
    J.L.F. Barbon, C.A. Fuertes, On the spectrum of nonrelativistic AdS/CFT. J. High Energy Phys. 0809, 030 (2008). arXiv:0806.3244 [hep-th] MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    B.S. Kim, D. Yamada, Properties of Schroedinger black holes from AdS space. J. High Energy Phys. 1107, 120 (2011). arXiv:1008.3286 [hep-th] MathSciNetADSCrossRefGoogle Scholar
  15. 15.
    T. Faulkner, N. Iqbal, H. Liu, J. McGreevy, D. Vegh, Strange metal transport realized by gauge/gravity duality. Science 329, 1043 (2010) ADSCrossRefGoogle Scholar
  16. 16.
    C. Charmousis, B. Gouteraux, B.S. Kim, E. Kiritsis, R. Meyer, Effective holographic theories for low-temperature condensed matter systems. J. High Energy Phys. 1011, 151 (2010). arXiv:1005.4690 [hep-th] ADSCrossRefGoogle Scholar
  17. 17.
    R.C. Myers, S. Sachdev, A. Singh, Holographic quantum critical transport without self-duality. Phys. Rev. D 83, 066017 (2011). arXiv:1010.0443 [hep-th] ADSCrossRefGoogle Scholar
  18. 18.
    S.S. Pal, Model building in AdS/CMT: DC conductivity and Hall angle. Phys. Rev. D 84, 126009 (2011). arXiv:1011.3117 [hep-th] ADSCrossRefGoogle Scholar
  19. 19.
    B.-H. Lee, D.-W. Pang, C. Park, Strange metallic behavior in anisotropic background. J. High Energy Phys. 1007, 057 (2010). arXiv:1006.1719 [hep-th] ADSCrossRefGoogle Scholar
  20. 20.
    R. Meyer, B. Gouteraux, B.S. Kim, Strange metallic behaviour and the thermodynamics of charged dilatonic black holes. Fortschr. Phys. 59, 741 (2011). arXiv:1102.4433 [hep-th] MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    B.-H. Lee, D.-W. Pang, Notes on properties of holographic strange metals. Phys. Rev. D 82, 104011 (2010). arXiv:1006.4915 [hep-th] ADSCrossRefGoogle Scholar
  22. 22.
    S.A. Hartnoll, J. Polchinski, E. Silverstein, D. Tong, Towards strange metallic holography Google Scholar
  23. 23.
    B.S. Kim, E. Kiritsis, C. Panagopoulos, Holographic quantum criticality and strange metal transport. New J. Phys. 14, 043045 (2012). arXiv:1012.3464 [cond-mat.str-el] ADSCrossRefGoogle Scholar
  24. 24.
    K.-Y. Kim, D.-W. Pang, Holographic DC conductivities from the open string metric. J. High Energy Phys. 1109, 051 (2011). arXiv:1108.3791 [hep-th] ADSCrossRefGoogle Scholar
  25. 25.
    M. Ali-Akbari, K.B. Fadafan, Conductivity at finite ’t Hooft coupling from AdS/CFT. arXiv:1008.2430 [hep-th]
  26. 26.
    M. Ammon, C. Hoyos, A. O’Bannon, J.M.S. Wu, Holographic flavor transport in Schrodinger spacetime. J. High Energy Phys. 1006, 012 (2010). arXiv:1003.5913 [hep-th] ADSCrossRefGoogle Scholar
  27. 27.
    A. Karch, A. O’Bannon, Metallic AdS/CFT. J. High Energy Phys. 0709, 024 (2007). arXiv:0705.3870 [hep-th] MathSciNetADSCrossRefGoogle Scholar
  28. 28.
    O. Aharony, O. Bergman, D.L. Jafferis, J. Maldacena, N=6 superconformal Chern–Simons-matter theories, M2-branes and their gravity duals. J. High Energy Phys. 0810, 091 (2008). arXiv:0806.1218 [hep-th] MathSciNetADSCrossRefGoogle Scholar
  29. 29.
    J. Pawelczyk, S. Theisen, AdS5×S5 black hole metric at O(α ′3). J. High Energy Phys. 9809, 010 (1998). hep-th/9808126 MathSciNetADSCrossRefGoogle Scholar
  30. 30.
    T. Banks, M.B. Green, Non-perturbative effects in AdS(5)×S5 string theory and d=4 SUSY Yang–Mills. J. High Energy Phys. 9805, 002 (1998). arXiv:hep-th/9804170 MathSciNetADSCrossRefGoogle Scholar
  31. 31.
    S.S. Gubser, I.R. Klebanov, A.A. Tseytlin, Coupling constant dependence in the thermodynamics of N=4 supersymmetric Yang–Mills theory. Nucl. Phys. B 534, 202 (1998). hep-th/9805156 MathSciNetADSMATHCrossRefGoogle Scholar
  32. 32.
    R.G. Cai, Gauss–Bonnet black holes in AdS spaces. Phys. Rev. D 65, 084014 (2002). arXiv:hep-th/0109133 MathSciNetADSCrossRefGoogle Scholar
  33. 33.
    S. Nojiri, S.D. Odintsov, Anti-de Sitter black hole thermodynamics in higher derivative gravity and new confining–deconfining phases in dual CFT. Phys. Lett. B 521, 87 (2001) [Erratum: Phys. Lett. B 542, 301 (2002)]. arXiv:hep-th/0109122 MathSciNetADSMATHCrossRefGoogle Scholar
  34. 34.
    S. Nojiri, S.D. Odintsov, (Anti-)de Sitter black holes in higher derivative gravity and dual conformal field theories. Phys. Rev. D 66, 044012 (2002). arXiv:hep-th/0204112 MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013

Authors and Affiliations

  1. 1.Physics DepartmentShahrood University of TechnologyShahroodIran

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