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Journal of High Energy Physics

, 2014:85 | Cite as

Resolving Lifshitz horizons

  • Sarah HarrisonEmail author
  • Shamit Kachru
  • Huajia Wang
Open Access
Article

Abstract

Via the AdS/CFT correspondence, ground states of field theories at finite charge density are mapped to extremal black brane solutions. Studies of simple gravity + matter systems in this context have uncovered wide new classes of extremal geometries. The Lifshitz metrics characterising field theories with non-trivial dynamical critical exponent z ≠ 1 emerge as one common endpoint in doped holographic toy models. However, the Lifshitz horizon exhibits mildly singular behaviour - while curvature invariants are finite, there are diverging tidal forces. Here we show that in some of the simplest contexts where Lifshitz metrics emerge, Einstein-Maxwell-dilaton theories, toy models of generic corrections can lead (presumably as one possibility among many) to a replacement of the Lifshitz metric, in the deep infrared, by a re-emergent AdS 2 × R 2 geometry. Thus, at least in these cases, the Lifshitz scaling characterises the physics over a wide range of energy scales, but the mild singularity is cured by quantum or stringy effects.

Keywords

AdS-CFT Correspondence Holography and condensed matter physics (AdS/CMT) 

Notes

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.

References

  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]
    J. McGreevy, Holographic duality with a view toward many-body physics, Adv. High Energy Phys. 2010 (2010) 723105 [arXiv:0909.0518] [INSPIRE].CrossRefGoogle Scholar
  4. [4]
    S. Sachdev, What can gauge-gravity duality teach us about condensed matter physics?, Ann. Rev. Condensed Matter Phys. 3 (2012) 9 [arXiv:1108.1197] [INSPIRE].CrossRefGoogle Scholar
  5. [5]
    N. Iizuka et al., Bianchi attractors: a classification of extremal black brane geometries, JHEP 07 (2012) 193 [arXiv:1201.4861] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  6. [6]
    S. Kachru, X. Liu and M. Mulligan, Gravity duals of Lifshitz-like fixed points, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725] [INSPIRE].ADSMathSciNetGoogle Scholar
  7. [7]
    S.A. Hartnoll, J. Polchinski, E. Silverstein and D. Tong, Towards strange metallic holography, JHEP 04 (2010) 120 [arXiv:0912.1061] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    K. Balasubramanian and K. Narayan, Lifshitz spacetimes from AdS null and cosmological solutions, JHEP 08 (2010) 014 [arXiv:1005.3291] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  9. [9]
    A. Donos and J.P. Gauntlett, Lifshitz solutions of D = 10 and D = 11 supergravity, JHEP 12 (2010) 002 [arXiv:1008.2062] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  10. [10]
    R. Gregory, S.L. Parameswaran, G. Tasinato and I. Zavala, Lifshitz solutions in supergravity and string theory, JHEP 12 (2010) 047 [arXiv:1009.3445] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  11. [11]
    A. Donos, J.P. Gauntlett, N. Kim and O. Varela, Wrapped M 5-branes, consistent truncations and AdS/CMT, JHEP 12 (2010) 003 [arXiv:1009.3805] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  12. [12]
    D. Cassani and A.F. Faedo, Constructing Lifshitz solutions from AdS, JHEP 05 (2011) 013 [arXiv:1102.5344] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  13. [13]
    N. Halmagyi, M. Petrini and A. Zaffaroni, Non-relativistic solutions of N = 2 gauged supergravity, JHEP 08 (2011) 041 [arXiv:1102.5740] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  14. [14]
    K. Copsey and R. Mann, Pathologies in asymptotically Lifshitz spacetimes, JHEP 03 (2011) 039 [arXiv:1011.3502] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  15. [15]
    G.T. Horowitz and B. Way, Lifshitz singularities, Phys. Rev. D 85 (2012) 046008 [arXiv:1111.1243] [INSPIRE].ADSGoogle Scholar
  16. [16]
    G.T. Horowitz and S.F. Ross, Naked black holes, Phys. Rev. D 56 (1997) 2180 [hep-th/9704058] [INSPIRE].ADSMathSciNetGoogle Scholar
  17. [17]
    K. Goldstein, S. Kachru, S. Prakash and S.P. Trivedi, Holography of charged dilaton black holes, JHEP 08 (2010) 078 [arXiv:0911.3586] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  18. [18]
    K. Goldstein et al., Holography of dyonic dilaton black branes, JHEP 10 (2010) 027 [arXiv:1007.2490] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    M. Taylor, Non-relativistic holography, arXiv:0812.0530 [INSPIRE].
  20. [20]
    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].ADSCrossRefMathSciNetGoogle Scholar
  21. [21]
    M. Cadoni and P. Pani, Holography of charged dilatonic black branes at finite temperature, JHEP 04 (2011) 049 [arXiv:1102.3820] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    C. Charmousis, B. Gouteraux, B.S. 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
  23. [23]
    E. Perlmutter, Domain wall holography for finite temperature scaling solutions, JHEP 02 (2011) 013 [arXiv:1006.2124] [INSPIRE].ADSGoogle Scholar
  24. [24]
    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
  25. [25]
    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
  26. [26]
    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
  27. [27]
    P. Berglund, J. Bhattacharyya and D. Mattingly, Charged dilatonic AdS black branes in arbitrary dimensions, JHEP 08 (2012) 042 [arXiv:1107.3096] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  28. [28]
    S.A. Hartnoll and A. Tavanfar, Electron stars for holographic metallic criticality, Phys. Rev. D 83 (2011) 046003 [arXiv:1008.2828] [INSPIRE].ADSGoogle Scholar
  29. [29]
    S.A. Hartnoll and P. Petrov, Electron star birth: a continuous phase transition at nonzero density, Phys. Rev. Lett. 106 (2011) 121601 [arXiv:1011.6469] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    S.A. Hartnoll, D.M. Hofman and D. Vegh, Stellar spectroscopy: Fermions and holographic Lifshitz criticality, JHEP 08 (2011) 096 [arXiv:1105.3197] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    B. Gouteraux and E. Kiritsis, Generalized holographic quantum criticality at finite density, JHEP 12 (2011) 036 [arXiv:1107.2116] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    S. Barisch, G. Lopes Cardoso, M. Haack, S. Nampuri and N.A. Obers, Nernst branes in gauged supergravity, JHEP 11 (2011) 090 [arXiv:1108.0296] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  33. [33]
    A. Dabholkar, R. Kallosh and A. Maloney, A stringy cloak for a classical singularity, JHEP 12 (2004) 059 [hep-th/0410076] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  34. [34]
    A. Donos, J.P. Gauntlett and C. Pantelidou, Spatially modulated instabilities of magnetic black branes, JHEP 01 (2012) 061 [arXiv:1109.0471] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    N. Bao, X. Dong, S. Harrison and E. Silverstein, The benefits of stress: resolution of the Lifshitz singularity, Phys. Rev. D 86 (2012) 106008 [arXiv:1207.0171] [INSPIRE].ADSGoogle Scholar
  36. [36]
    N. Ogawa, T. Takayanagi and T. Ugajin, Holographic Fermi surfaces and entanglement entropy, JHEP 01 (2012) 125 [arXiv:1111.1023] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  37. [37]
    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].ADSCrossRefGoogle Scholar
  38. [38]
    E. Shaghoulian, Holographic entanglement entropy and Fermi surfaces, JHEP 05 (2012) 065 [arXiv:1112.2702] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  39. [39]
    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
  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]
    K. Jensen, S. Kachru, A. Karch, J. Polchinski and E. Silverstein, Towards a holographic marginal Fermi liquid, Phys. Rev. D 84 (2011) 126002 [arXiv:1105.1772] [INSPIRE].ADSGoogle Scholar

Copyright information

© The Author(s) 2014

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Stanford Institute for Theoretical Physics, Department of PhysicsStanford UniversityStanfordU.S.A
  2. 2.Theory Group, SLAC National Accelerator LaboratoryMenlo ParkU.S.A

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