Infrared behavior of scalar condensates in effective holographic theories

Article

Abstract

We investigate the infrared behavior of the spectrum of scalar-dressed, asymptotically Anti de Sitter (AdS) black brane (BB) solutions of effective holographic models. These solutions describe scalar condensates in the dual field theories. We show that for zero charge density the ground state of these BBs must be degenerate with the AdS vacuum, must satisfy conformal boundary conditions for the scalar field and it is isolated from the continuous part of the spectrum. When a finite charge density is switched on, the ground state is not anymore isolated and the degeneracy is removed. Depending on the coupling functions, the new ground state may possibly be energetically preferred with respect to the extremal Reissner-Nordstrom AdS BB. We derive several properties of BBs near extremality and at finite temperature. As a check and illustration of our results we derive and discuss several analytic and numerical, BB solutions of Einstein-scalar-Maxwell AdS gravity with different coupling functions and different potentials. We also discuss how our results can be used for understanding holographic quantum critical points, in particular their stability and the associated quantum phase transitions leading to superconductivity or hyperscaling violation.

Keywords

Holography and condensed matter physics (AdS/CMT) Black Holes 

References

  1. [1]
    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  3. [3]
    G.T. Horowitz and M.M. Roberts, Holographic Superconductors with Various Condensates, Phys. Rev. D 78 (2008) 126008 [arXiv:0810.1077] [INSPIRE].ADSGoogle Scholar
  4. [4]
    C.P. Herzog, Lectures on Holographic Superfluidity and Superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].Google Scholar
  5. [5]
    S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    C. Charmousis, B. Gouteraux and J. Soda, Einstein-Maxwell-Dilaton theories with a Liouville potential, Phys. Rev. D 80 (2009) 024028 [arXiv:0905.3337] [INSPIRE].MathSciNetADSGoogle Scholar
  7. [7]
    M. Cadoni, G. D’Appollonio and P. Pani, Phase transitions between Reissner-Nordstrom and dilatonic black holes in 4D AdS spacetime, JHEP 03 (2010) 100 [arXiv:0912.3520] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  8. [8]
    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
  9. [9]
    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
  10. [10]
    K. Goldstein et al., Holography of Dyonic Dilaton Black Branes, JHEP 10 (2010) 027 [arXiv:1007.2490] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    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
  12. [12]
    G. Bertoldi, B.A. Burrington and A.W. Peet, Thermal behavior of charged dilatonic black branes in AdS and UV completions of Lifshitz-like geometries, Phys. Rev. D 82 (2010) 106013 [arXiv:1007.1464] [INSPIRE].ADSGoogle Scholar
  13. [13]
    B. Gouteraux and E. Kiritsis, Generalized Holographic Quantum Criticality at Finite Density, JHEP 12 (2011) 036 [arXiv:1107.2116] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    N. Iizuka, N. Kundu, P. Narayan and S.P. Trivedi, Holographic Fermi and Non-Fermi Liquids with Transitions in Dilaton Gravity, JHEP 01 (2012) 094 [arXiv:1105.1162] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    M. Cadoni and P. Pani, Holography of charged dilatonic black branes at finite temperature, JHEP 04 (2011) 049 [arXiv:1102.3820] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    S.A. Hartnoll, Horizons, holography and condensed matter, arXiv:1106.4324 [INSPIRE].
  17. [17]
    B.-H. Lee, D.-W. Pang and C. Park, A holographic model of strange metals, Int. J. Mod. Phys. A 26 (2011) 2279 [arXiv:1107.5822] [INSPIRE].ADSGoogle Scholar
  18. [18]
    B.S. Kim, Schródinger holography with and without hyperscaling violation, JHEP 06 (2012) 116 [arXiv:1202.6062] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    X. Dong, S. Harrison, S. Kachru, G. Torroba and H. Wang, Aspects of holography for theories with hyperscaling violation, JHEP 06 (2012) 041 [arXiv:1201.1905] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    J.-P. Wu and H.-B. Zeng, Dynamic gap from holographic fermions in charged dilaton black branes, JHEP 04 (2012) 068 [arXiv:1201.2485] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    K. Hashimoto and N. Iizuka, A Comment on Holographic Luttinger Theorem, JHEP 07 (2012) 064 [arXiv:1203.5388] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    M. Ammon, M. Kaminski and A. Karch, Hyperscaling-Violation on Probe D-branes, JHEP 11 (2012) 028 [arXiv:1207.1726] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    N. Iizuka and K. Maeda, Study of Anisotropic Black Branes in Asymptotically anti-de Sitter, JHEP 07 (2012) 129 [arXiv:1204.3008] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    P. Dey and S. Roy, Intersecting D-branes and Lifshitz-like space-time, Phys. Rev. D 86 (2012) 066009 [arXiv:1204.4858] [INSPIRE].ADSGoogle Scholar
  25. [25]
    C. Park, Membrane paradigm in the Einstein-dilaton theory, arXiv:1209.0842 [INSPIRE].
  26. [26]
    Y.S. Myung and T. Moon, Quasinormal frequencies and thermodynamic quantities for the Lifshitz black holes, Phys. Rev. D 86 (2012) 024006 [arXiv:1204.2116] [INSPIRE].ADSGoogle Scholar
  27. [27]
    A. Adam, B. Crampton, J. Sonner and B. Withers, Bosonic Fractionalisation Transitions, JHEP 01 (2013) 127 [arXiv:1208.3199] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    B. Gouteraux and E. Kiritsis, Quantum critical lines in holographic phases with (un)broken symmetry, JHEP 04 (2013) 053 [arXiv:1212.2625] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    A. Salvio, Holographic Superfluids and Superconductors in Dilaton-Gravity, JHEP 09 (2012) 134 [arXiv:1207.3800] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    M. Cadoni and S. Mignemi, Phase transition and hyperscaling violation for scalar Black Branes, JHEP 06 (2012) 056 [arXiv:1205.0412] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    M. Cadoni and M. Serra, Hyperscaling violation for scalar black branes in arbitrary dimensions, arXiv:1209.4484 [INSPIRE].
  32. [32]
    N. Ogawa, T. Takayanagi and T. Ugajin, Holographic Fermi Surfaces and Entanglement Entropy, JHEP 01 (2012) 125 [arXiv:1111.1023] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  33. [33]
    L. Huijse, S. Sachdev and B. Swingle, Hidden Fermi surfaces in compressible states of gauge-gravity duality, Phys. Rev. B 85 (2012) 035121 [arXiv:1112.0573] [INSPIRE].ADSGoogle Scholar
  34. [34]
    J. Gath, J. Hartong, R. Monteiro and N.A. Obers, Holographic Models for Theories with Hyperscaling Violation, arXiv:1212.3263 [INSPIRE].
  35. [35]
    K. Narayan, On Lifshitz scaling and hyperscaling violation in string theory, Phys. Rev. D 85 (2012) 106006 [arXiv:1202.5935] [INSPIRE].ADSGoogle Scholar
  36. [36]
    K. Narayan, T. Takayanagi and S.P. Trivedi, AdS plane waves and entanglement entropy, JHEP 04 (2013) 051 [arXiv:1212.4328] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    K. Narayan, Non-conformal brane plane waves and entanglement entropy, arXiv:1304.6697 [INSPIRE].
  38. [38]
    P. Breitenlohner and D.Z. Freedman, Positive Energy in anti-de Sitter Backgrounds and Gauged Extended Supergravity, Phys. Lett. B 115 (1982) 197 [INSPIRE].MathSciNetADSGoogle Scholar
  39. [39]
    T. Torii, K. Maeda and M. Narita, Scalar hair on the black hole in asymptotically anti-de Sitter space-time, Phys. Rev. D 64 (2001) 044007 [INSPIRE].MathSciNetADSGoogle Scholar
  40. [40]
    T. Hertog, Towards a Novel no-hair Theorem for Black Holes, Phys. Rev. D 74 (2006) 084008 [gr-qc/0608075] [INSPIRE].MathSciNetADSGoogle Scholar
  41. [41]
    M. Cadoni, S. Mignemi and M. Serra, Exact solutions with AdS asymptotics of Einstein and Einstein-Maxwell gravity minimally coupled to a scalar field, Phys. Rev. D 84 (2011) 084046 [arXiv:1107.5979] [INSPIRE].ADSGoogle Scholar
  42. [42]
    M. Cadoni, S. Mignemi and M. Serra, Black brane solutions and their solitonic extremal limit in Einstein-scalar gravity, Phys. Rev. D 85 (2012) 086001 [arXiv:1111.6581] [INSPIRE].ADSGoogle Scholar
  43. [43]
    T. Hertog and K. Maeda, Black holes with scalar hair and asymptotics in N = 8 supergravity, JHEP 07 (2004) 051 [hep-th/0404261] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  44. [44]
    E. Witten, Multitrace operators, boundary conditions and AdS/CFT correspondence, hep-th/0112258 [INSPIRE].
  45. [45]
    O. Aharony, M. Berkooz and E. Silverstein, Multiple trace operators and nonlocal string theories, JHEP 08 (2001) 006 [hep-th/0105309] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  46. [46]
    M. Berkooz, A. Sever and A. Shomer, ’Double tracedeformations, boundary conditions and space-time singularities, JHEP 05 (2002) 034 [hep-th/0112264] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  47. [47]
    D. Marolf and S.F. Ross, Boundary Conditions and New Dualities: Vector Fields in AdS/CFT, JHEP 11 (2006) 085 [hep-th/0606113] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  48. [48]
    T. Hartman and L. Rastelli, Double-trace deformations, mixed boundary conditions and functional determinants in AdS/CFT, JHEP 01 (2008) 019 [hep-th/0602106] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  49. [49]
    L. Vecchi, Multitrace deformations, Gamow states and Stability of AdS/CFT, JHEP 04 (2011) 056 [arXiv:1005.4921] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  50. [50]
    T. Hertog and G.T. Horowitz, Designer gravity and field theory effective potentials, Phys. Rev. Lett. 94 (2005) 221301 [hep-th/0412169] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  51. [51]
    C. Martinez, R. Troncoso and J. Zanelli, Exact black hole solution with a minimally coupled scalar field, Phys. Rev. D 70 (2004) 084035 [hep-th/0406111] [INSPIRE].MathSciNetADSGoogle Scholar
  52. [52]
    G.T. Horowitz and M.M. Roberts, Zero Temperature Limit of Holographic Superconductors, JHEP 11 (2009) 015 [arXiv:0908.3677] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  1. 1.Dipartimento di Fisica, Università di Cagliari and INFN, Sezione di Cagliari, Cittadella UniversitariaMonserratoItaly
  2. 2.CENTRA, Departamento de Física, Instituto Superior Técnico, Universidade Técnica de Lisboa - UTLLisboaPortugal
  3. 3.Institute for Theory & Computation, Harvard-Smithsonian CfACambridgeU.S.A.

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