Journal of High Energy Physics

, 2012:34 | Cite as

On holography with hyperscaling violation



We study certain features of strongly coupled theories with hyperscaling violation by making use of their gravitational duals. We will consider models with an anisotropic scaling in time or in one of spatial directions. In particular for the case where the anisotropic scaling is along a spatial direction we will compute the holographic entanglement entropy and show that for specific values of the parameters it exhibits a logarithmic violation of the area law. We will also probe the backgrounds by different closed and open strings which in turn can be used to read, for example, effective potential of an external object, drag force and etc.


AdS-CFT Correspondence 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) 1113] [hep-th/9711200] [INSPIRE].MathSciNetADSMATHGoogle 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].MathSciNetADSMATHGoogle Scholar
  4. [4]
    S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    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
  6. [6]
    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
  7. [7]
    M. Taylor, Non-relativistic holography, arXiv:0812.0530 [INSPIRE].
  8. [8]
    D. Son, Toward an AdS/cold atoms correspondence: a geometric realization of the Schrödinger symmetry, Phys. Rev. D 78 (2008) 046003 [arXiv:0804.3972] [INSPIRE].MathSciNetADSGoogle Scholar
  9. [9]
    K. Balasubramanian and J. McGreevy, Gravity duals for non-relativistic CFTs, Phys. Rev. Lett. 101 (2008) 061601 [arXiv:0804.4053] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  10. [10]
    M. Alishahiha and O.J. Ganor, Twisted backgrounds, pp waves and nonlocal field theories, JHEP 03 (2003) 006 [hep-th/0301080] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  11. [11]
    E. Perlmutter, Domain wall holography for finite temperature scaling solutions, JHEP 02 (2011) 013 [arXiv:1006.2124] [INSPIRE].ADSGoogle 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]
    G. Bertoldi, B.A. Burrington, A.W. Peet and I.G. Zadeh, Lifshitz-like black brane thermodynamics in higher dimensions, Phys. Rev. D 83 (2011) 126006 [arXiv:1101.1980] [INSPIRE].ADSGoogle Scholar
  14. [14]
    K. Goldstein, N. Iizuka, S. Kachru, S. Prakash, S.P. Trivedi, et al., Holography of dyonic dilaton black branes, JHEP 10 (2010) 027 [arXiv:1007.2490] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    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
  16. [16]
    P. Berglund, J. Bhattacharyya and D. Mattingly, Charged dilatonic AdS black branes in arbitrary dimensions, JHEP 08 (2012) 042 [arXiv:1107.3096] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    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
  18. [18]
    B. Gouteraux and E. Kiritsis, Generalized holographic quantum criticality at finite density, JHEP 12 (2011) 036 [arXiv:1107.2116] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    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
  20. [20]
    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
  21. [21]
    N. Ogawa, T. Takayanagi and T. Ugajin, Holographic Fermi surfaces and entanglement entropy, JHEP 01 (2012) 125 [arXiv:1111.1023] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    J. Bhattacharya, S. Cremonini and A. Sinkovics, On the IR completion of geometries with hyperscaling violation, arXiv:1208.1752 [INSPIRE].
  23. [23]
    N. Kundu, P. Narayan, N. Sircar and S.P. Trivedi, Entangled dilaton dyons, arXiv:1208.2008 [INSPIRE].
  24. [24]
    M. Fujita, T. Nishioka and T. Takayanagi, Geometric entropy and Hagedorn/deconfinement transition, JHEP 09 (2008) 016 [arXiv:0806.3118] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  25. [25]
    I. Bah, L.A. Pando Zayas and C.A. Terrero-Escalante, Holographic geometric entropy at finite temperature from black holes in global Anti de Sitter spaces, Int. J. Mod. Phys. A 27 (2012) 1250048 [arXiv:0809.2912] [INSPIRE].ADSGoogle Scholar
  26. [26]
    S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  27. [27]
    S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  28. [28]
    J. de Boer, M. Kulaxizi and A. Parnachev, Holographic entanglement entropy in Lovelock gravities, JHEP 07 (2011) 109 [arXiv:1101.5781] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    S.-J. Rey and J.-T. Yee, Macroscopic strings as heavy quarks in large-N gauge theory and Anti-de Sitter supergravity, Eur. Phys. J. C 22 (2001) 379 [hep-th/9803001] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  30. [30]
    J.M. Maldacena, Wilson loops in large-N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  31. [31]
    S.S. Gubser, Drag force in AdS/CFT, Phys. Rev. D 74 (2006) 126005 [hep-th/0605182] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  32. [32]
    E. Kiritsis, Lorentz violation, gravity, dissipation and holography, arXiv:1207.2325 [INSPIRE].
  33. [33]
    A. Akhavan, M. Alishahiha, A. Davody and A. Vahedi, Non-relativistic CFT and semi-classical strings, JHEP 03 (2009) 053 [arXiv:0811.3067] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  34. [34]
    K.B. Fadafan, Drag force in asymptotically Lifshitz spacetimes, arXiv:0912.4873 [INSPIRE].
  35. [35]
    U. Gürsoy, E. Kiritsis, L. Mazzanti and F. Nitti, Langevin diffusion of heavy quarks in non-conformal holographic backgrounds, JHEP 12 (2010) 088 [arXiv:1006.3261] [INSPIRE].CrossRefGoogle Scholar
  36. [36]
    K.B. Fadafan, H. Liu, K. Rajagopal and U.A. Wiedemann, Stirring strongly coupled plasma, Eur. Phys. J. C 61 (2009) 553 [arXiv:0809.2869] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    C. Athanasiou, P.M. Chesler, H. Liu, D. Nickel and K. Rajagopal, Synchrotron radiation in strongly coupled conformal field theories, Phys. Rev. D 81 (2010) 126001 [Erratum ibid. D 84 (2011)069901] [arXiv:1001.3880] [INSPIRE].ADSGoogle Scholar
  38. [38]
    K.B. Fadafan and H. Soltanpanahi, Energy loss in a strongly coupled anisotropic plasma, JHEP 10 (2012) 085 [arXiv:1206.2271] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    M. Ali-Akbari and U. Gürsoy, Rotating strings and energy loss in non-conformal holography, JHEP 01 (2012) 105 [arXiv:1110.5881] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    K. Narayan, On Lifshitz scaling and hyperscaling violation in string theory, Phys. Rev. D 85 (2012) 106006 [arXiv:1202.5935] [INSPIRE].ADSGoogle Scholar
  41. [41]
    M. Ammon, M. Kaminski and A. Karch, Hyperscaling-violation on probe D-branes, arXiv:1207.1726 [INSPIRE].
  42. [42]
    S. Gubser, I. Klebanov and A.M. Polyakov, A semiclassical limit of the gauge/string correspondence, Nucl. Phys. B 636 (2002) 99 [hep-th/0204051] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  43. [43]
    J.A. Minahan, Circular semiclassical string solutions on AdS 5 × S 5, Nucl. Phys. B 648 (2003) 203 [hep-th/0209047] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  44. [44]
    M. Alishahiha and A.E. Mosaffa, Circular semiclassical string solutions on confining AdS/CFT backgrounds, JHEP 10 (2002) 060 [hep-th/0210122] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  1. 1.School of physicsInstitute for Research in Fundamental Sciences (IPM)TehranIran
  2. 2.Department of PhysicsKyung-Hee UniversitySeoulKorea

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