Holographic Fermi and non-Fermi liquids with transitions in dilaton gravity

  • Norihiro Iizuka
  • Nilay Kundu
  • Prithvi Narayan
  • Sandip P. Trivedi
Open Access


We study the two-point function for fermionic operators in a class of strongly coupled systems using the gauge-gravity correspondence. The gravity description includes a gauge field and a dilaton which determines the gauge coupling and the potential energy. Extremal black brane solutions in this system typically have vanishing entropy. By analyzing a charged fermion in these extremal black brane backgrounds we calculate the two-point function of the corresponding boundary fermionic operator. We find that in some region of parameter space it is of Fermi liquid type. Outside this region no well-defined quasi-particles exist, with the excitations acquiring a non-vanishing width at zero frequency. At the transition, the two-point function can exhibit non-Fermi liquid behaviour.


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


  1. [[1]
    J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1133] [hep-th/9711200] [INSPIRE].MathSciNetADSzbMATHGoogle Scholar
  2. [[2]
    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].MathSciNetADSGoogle Scholar
  3. [[3]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].MathSciNetADSzbMATHGoogle Scholar
  4. [[4]
    S.-S. Lee, A Non-Fermi Liquid from a Charged Black Hole: A Critical Fermi Ball, Phys. Rev. D 79 (2009) 086006 [arXiv:0809.3402] [INSPIRE].ADSGoogle Scholar
  5. [[5]
    H. Liu, J. McGreevy and D. Vegh, Non-Fermi liquids from holography, Phys. Rev. D 83 (2011) 065029 [arXiv:0903.2477] [INSPIRE].ADSGoogle Scholar
  6. [[6]
    M. Cubrovic, J. Zaanen and K. Schalm, String Theory, Quantum Phase Transitions and the Emergent Fermi-Liquid, Science 325 (2009) 439 [arXiv:0904.1993] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  7. [[7]
    T. Faulkner, H. Liu, J. McGreevy and D. Vegh, Emergent quantum criticality, Fermi surfaces and AdS 2, Phys. Rev. D 83 (2011) 125002 [arXiv:0907.2694] [INSPIRE].ADSGoogle Scholar
  8. [[8]
    T. Faulkner, N. Iqbal, H. Liu, J. McGreevy and D. Vegh, From Black Holes to Strange Metals, arXiv:1003.1728 [INSPIRE].
  9. [[9]
    T. Faulkner, N. Iqbal, H. Liu, J. McGreevy and D. Vegh, Holographic non-Fermi liquid fixed points, arXiv:1101.0597 [INSPIRE].
  10. [[10]
    A. Dabholkar, A. Sen and S.P. Trivedi, Black hole microstates and attractor without supersymmetry, JHEP 01 (2007) 096 [hep-th/0611143] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  11. [[11]
    S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [INSPIRE].ADSGoogle Scholar
  12. [[12]
    S.S. Gubser and F.D. Rocha, Peculiar properties of a charged dilatonic black hole in AdS 5, Phys. Rev. D 81 (2010) 046001 [arXiv:0911.2898] [INSPIRE].MathSciNetADSGoogle Scholar
  13. [[13]
    K. Goldstein, S. Kachru, S. Prakash and S.P. Trivedi, Holography of Charged Dilaton Black Holes, JHEP 08 (2010) 078 [arXiv:0911.3586] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  14. [[14]
    K. Goldstein, N. Iizuka, S. Kachru, S. Prakash, S.P. Trivedi and A. Westphal, Holography of Dyonic Dilaton Black Branes, JHEP 10 (2010) 027 [arXiv:1007.2490] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [[15]
    C. Charmousis, B. Gouteraux, B. Kim, E. Kiritsis and R. Meyer, Effective Holographic Theories for low-temperature condensed matter systems, JHEP 11 (2010) 151 [arXiv:1005.4690] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [[16]
    R. Meyer, B. Gouteraux and B.S. Kim, Strange Metallic Behaviour and the Thermodynamics of Charged Dilatonic Black Holes, Fortsch. Phys. 59 (2011) 741 [arXiv:1102.4433] [INSPIRE].MathSciNetADSzbMATHCrossRefGoogle Scholar
  17. [[17]
    B. Gouteraux, B.S. Kim and R. Meyer, Charged Dilatonic Black Holes and their Transport Properties, Fortsch. Phys. 59 (2011) 723 [arXiv:1102.4440] [INSPIRE].MathSciNetADSzbMATHCrossRefGoogle Scholar
  18. [[18]
    T. Faulkner and J. Polchinski, Semi-Holographic Fermi Liquids, JHEP 06 (2011) 012 [arXiv:1001.5049] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  19. [[19]
    S. Prakash and S.P. Trivedi, unpublished notes.Google Scholar
  20. [[20]
    S. Sachdev, Holographic metals and the fractionalized Fermi liquid, Phys. Rev. Lett. 105 (2010) 151602 [arXiv:1006.3794] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [[21]
    S. Sachdev, The landscape of the Hubbard model, arXiv:1012.0299 [INSPIRE].
  22. [[22]
    L. Huijse and S. Sachdev, Fermi surfaces and gauge-gravity duality, Phys. Rev. D 84 (2011) 026001 [arXiv:1104.5022] [INSPIRE].ADSGoogle Scholar
  23. [[23]
    T. Senthil, Critical Fermi surfaces and non-Fermi liquid metals, Phys. Rev. B 78 (2008) 035103 [arXiv:0803.4009].ADSGoogle Scholar
  24. [[24]
    S. Kachru, A. Karch and S. Yaida, Adventures in Holographic Dimer Models, New J. Phys. 13 (2011) 035004 [arXiv:1009.3268] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [[25]
    S. Kachru, A. Karch and S. Yaida, Holographic Lattices, Dimers and Glasses, Phys. Rev. D 81 (2010) 026007 [arXiv:0909.2639] [INSPIRE].MathSciNetADSGoogle Scholar
  26. [[26]
    M. Kulaxizi and A. Parnachev, Holographic Responses of Fermion Matter, Nucl. Phys. B 815 (2009) 125 [arXiv:0811.2262] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  27. [[27]
    S.A. Hartnoll, J. Polchinski, E. Silverstein and D. Tong, Towards strange metallic holography, JHEP 04 (2010) 120 [arXiv:0912.1061] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [[28]
    K. Goldstein, N. Iizuka, R.P. Jena and S.P. Trivedi, Non-supersymmetric attractors, Phys. Rev. D 72 (2005) 124021 [hep-th/0507096] [INSPIRE].MathSciNetADSGoogle Scholar
  29. [[29]
    M. Taylor, Non-relativistic holography, arXiv:0812.0530 [INSPIRE].
  30. [[30]
    S. Kachru, X. Liu and M. Mulligan, Gravity Duals of Lifshitz-like Fixed Points, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725] [INSPIRE].MathSciNetADSGoogle Scholar
  31. [[31]
    P. Koroteev and M. Libanov, On Existence of Self-Tuning Solutions in Static Braneworlds without Singularities, JHEP 02 (2008) 104 [arXiv:0712.1136] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  32. [[32]
    K. Balasubramanian and K. Narayan, Lifshitz spacetimes from AdS null and cosmological solutions, JHEP 08 (2010) 014 [arXiv:1005.3291] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  33. [[33]
    A. Donos and J.P. Gauntlett, Lifshitz Solutions of D = 10 and D = 11 supergravity, JHEP 12 (2010) 002 [arXiv:1008.2062] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  34. [[34]
    C.P. Herzog, P. Kovtun, S. Sachdev and D.T. Son, Quantum critical transport, duality and M-theory, Phys. Rev. D 75 (2007) 085020 [hep-th/0701036] [INSPIRE].MathSciNetADSGoogle Scholar
  35. [[35]
    G.T. Horowitz and M.M. Roberts, Zero Temperature Limit of Holographic Superconductors, JHEP 11 (2009) 015 [arXiv:0908.3677] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [[36]
    M. Edalati, J.I. Jottar and R.G. Leigh, Transport Coefficients at Zero Temperature from Extremal Black Holes, JHEP 01 (2010) 018 [arXiv:0910.0645] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [[37]
    S. Jain, Universal properties of thermal and electrical conductivity of gauge theory plasmas from holography, JHEP 06 (2010) 023 [arXiv:0912.2719] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [[38]
    S. Jain, Universal thermal and electrical conductivity from holography, JHEP 11 (2010) 092 [arXiv:1008.2944] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [[39]
    S.K. Chakrabarti, S. Chakrabortty and S. Jain, Proof of universality of electrical conductivity at finite chemical potential, JHEP 02 (2011) 073 [arXiv:1011.3499] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [[40]
    A.B. Migdal, Qualitative Methods in Quantum Theory, Addison Wesley Publishing Company, New York U.S.A. (1989) [ISBN: 0-201-09441-X].Google Scholar
  41. [[41]
    C.-M. Chen and D.-W. Pang, Holography of Charged Dilaton Black Holes in General Dimensions, JHEP 06 (2010) 093 [arXiv:1003.5064] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [[42]
    J.P. Gauntlett, J. Sonner and T. Wiseman, Quantum Criticality and Holographic Superconductors in M-theory, JHEP 02 (2010) 060 [arXiv:0912.0512] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  43. [[43]
    A. Donos, J.P. Gauntlett, N. Kim and O. Varela, Wrapped M5-branes, consistent truncations and AdS/CMT, JHEP 12 (2010) 003 [arXiv:1009.3805] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  44. [[44]
    M.A. Vasiliev, Higher spin gauge theories in four-dimensions, three-dimensions and two-dimensions, Int. J. Mod. Phys. D 5 (1996) 763 [hep-th/9611024] [INSPIRE].MathSciNetADSGoogle Scholar
  45. [[45]
    N. Iizuka, N. Kundu, P. Narayan and S.P. Trivedi, work in progress.Google Scholar
  46. [[46]
    S.A. Hartnoll and A. Tavanfar, Electron stars for holographic metallic criticality, Phys. Rev. D 83 (2011) 046003 [arXiv:1008.2828] [INSPIRE].ADSGoogle Scholar
  47. [[47]
    X. Arsiwalla, J. de Boer, K. Papadodimas and E. Verlinde, Degenerate Stars and Gravitational Collapse in AdS/CFT, JHEP 01 (2011) 144 [arXiv:1010.5784] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [[48]
    S. Ferrara, R. Kallosh and A. Strominger, N = 2 extremal black holes, Phys. Rev. D 52 (1995) 5412 [hep-th/9508072] [INSPIRE].MathSciNetADSGoogle Scholar
  49. [[49]
    S. Ferrara, G.W. Gibbons and R. Kallosh, Black holes and critical points in moduli space, Nucl. Phys. B 500 (1997) 75 [hep-th/9702103] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  50. [[50]
    G.W. Gibbons, R. Kallosh and B. Kol, Moduli, scalar charges and the first law of black hole thermodynamics, Phys. Rev. Lett. 77 (1996) 4992 [hep-th/9607108] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [[51]
    A. Sen, Black hole entropy function and the attractor mechanism in higher derivative gravity, JHEP 09 (2005) 038 [hep-th/0506177] [INSPIRE].ADSCrossRefGoogle Scholar
  52. [[52]
    R. Kallosh, N. Sivanandam and M. Soroush, The non-BPS black hole attractor equation, JHEP 03 (2006) 060 [hep-th/0602005] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  53. [[53]
    S. Bellucci, S. Ferrara, R. Kallosh and A. Marrani, Extremal black hole and flux vacua attractors, Lect. Notes Phys. 755 (2008) 115 [arXiv:0711.4547] [INSPIRE].MathSciNetADSGoogle Scholar
  54. [[54]
    S. Kachru, R. Kallosh and M. Shmakova, Generalized attractor points in gauged supergravity, Phys. Rev. D 84 (2011) 046003 [arXiv:1104.2884] [INSPIRE].ADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • Norihiro Iizuka
    • 1
  • Nilay Kundu
    • 2
  • Prithvi Narayan
    • 2
  • Sandip P. Trivedi
    • 2
  1. 1.Theory Division, CERNGeneva 23Switzerland
  2. 2.Tata Institute for Fundamental ResearchMumbaiIndia

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