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Hyperscaling violation from supergravity

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Abstract

In recent applications of AdS/CFT to condensed matter physics, a metric that transforms covariantly under dilatation has been argued to signal hyperscaling violation in a dual quantum field theory. We contextualize and introduce large, in some cases infinite, families of supergravity solutions with this property, focusing on scale covariant generalizations of AdS and Schrödinger spacetimes. These embeddings rely on various aspects of dimensional reduction and flux compactification of eleven-dimensional supergravity. Our top-down approach can be viewed as a partial holographic classification of the landscape of strongly coupled, UV complete quantum field theories with hyperscaling violation.

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References

  1. 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].

    Article  ADS  Google Scholar 

  2. 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].

    Article  ADS  Google Scholar 

  3. E. Shaghoulian, Holographic entanglement entropy and Fermi surfaces, JHEP 05 (2012) 065 [arXiv:1112.2702] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  4. S.A. Hartnoll and E. Shaghoulian, Spectral weight in holographic scaling geometries, arXiv:1203.4236 [INSPIRE].

  5. H. Singh, Lifshitz/Schrödinger Dp-branes and dynamical exponents, arXiv:1202.6533 [INSPIRE].

  6. K. Narayan, On Lifshitz scaling and hyperscaling violation in string theory, Phys. Rev. D 85 (2012) 106006 [arXiv:1202.5935] [INSPIRE].

    ADS  Google Scholar 

  7. P. Dey and S. Roy, Lifshitz-like space-time from intersecting branes in string/M theory, arXiv:1203.5381 [INSPIRE].

  8. P. Dey and S. Roy, Intersecting D-branes and Lifshitz-like space-time, arXiv:1204.4858 [INSPIRE].

  9. S. Kachru, X. Liu and M. Mulligan, Gravity duals of Lifshitz-like fixed points, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  10. P. Koroteev and M. Libanov, On existence of self-tuning solutions in static braneworlds without singularities, JHEP 02 (2008) 104 [arXiv:0712.1136] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  11. M. Taylor, Non-relativistic holography, arXiv:0812.0530 [INSPIRE].

  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].

    MathSciNet  ADS  Google Scholar 

  13. 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].

    Article  ADS  Google Scholar 

  14. E. Perlmutter, Domain wall holography for finite temperature scaling solutions, JHEP 02 (2011) 013 [arXiv:1006.2124] [INSPIRE].

    ADS  Google Scholar 

  15. H. Singh, Special limits and non-relativistic solutions, JHEP 12 (2010) 061 [arXiv:1009.0651] [INSPIRE].

    Article  ADS  Google Scholar 

  16. B.S. Kim, Schrödinger holography with and without hyperscaling violation, arXiv:1202.6062 [INSPIRE].

  17. 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].

    MathSciNet  ADS  Google Scholar 

  18. K. Balasubramanian and J. McGreevy, Gravity duals for non-relativistic CFTs, Phys. Rev. Lett. 101 (2008) 061601 [arXiv:0804.4053] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  19. L. Mazzucato, Y. Oz and S. Theisen, Non-relativistic branes, JHEP 04 (2009) 073 [arXiv:0810.3673] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  20. B. Gouteraux, J. Smolic, M. Smolic, K. Skenderis and M. Taylor, Holography for Einstein-Maxwell-dilaton theories from generalized dimensional reduction, JHEP 01 (2012) 089 [arXiv:1110.2320] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  21. S. Sachdev, The quantum phases of matter, arXiv:1203.4565 [INSPIRE].

  22. H. Lü, C. Pope and P. Townsend, Domain walls from Anti-de Sitter space-time, Phys. Lett. B 391 (1997) 39 [hep-th/9607164] [INSPIRE].

    Article  ADS  Google Scholar 

  23. P. Kraus and E. Perlmutter, Universality and exactness of Schrödinger geometries in string and M-theory, JHEP 05 (2011) 045 [arXiv:1102.1727] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. H. Lü, C. Pope, E. Sezgin and K. Stelle, Stainless super p-branes, Nucl. Phys. B 456 (1995) 669 [hep-th/9508042] [INSPIRE].

    Article  ADS  Google Scholar 

  25. B. Gouteraux and E. Kiritsis, Generalized holographic quantum criticality at finite density, JHEP 12 (2011) 036 [arXiv:1107.2116] [INSPIRE].

    Article  ADS  Google Scholar 

  26. H. Lü and C. Pope, P-brane solitons in maximal supergravities, Nucl. Phys. B 465 (1996) 127 [hep-th/9512012] [INSPIRE].

    Article  ADS  Google Scholar 

  27. H. Lü, C. Pope, T.A. Tran and K. Xu, Classification of p-branes, NUTs, waves and intersections, Nucl. Phys. B 511 (1998) 98 [hep-th/9708055] [INSPIRE].

    Article  ADS  Google Scholar 

  28. M. Cvetič, H. Lü and C. Pope, Domain walls with localized gravity and domain wall/QFT correspondence, Phys. Rev. D 63 (2001) 086004 [hep-th/0007209] [INSPIRE].

    ADS  Google Scholar 

  29. M. Duff, H. Lü and C. Pope, The black branes of M-theory, Phys. Lett. B 382 (1996) 73 DOI:dx.doi.org [hep-th/9604052] [INSPIRE].

    Article  ADS  Google Scholar 

  30. H. Lü and C. Pope, p-brane taxonomy, hep-th/9702086 [INSPIRE].

  31. I. Lavrinenko, H. Lü and C. Pope, From topology to generalized dimensional reduction, Nucl. Phys. B 492 (1997) 278 [hep-th/9611134] [INSPIRE].

    ADS  Google Scholar 

  32. J. Scherk and J.H. Schwarz, How to get masses from extra dimensions, Nucl. Phys. B 153 (1979) 61 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  33. M. Guica, K. Skenderis, M. Taylor and B.C. van Rees, Holography for Schrödinger backgrounds, JHEP 02 (2011) 056 [arXiv:1008.1991] [INSPIRE].

    Article  ADS  Google Scholar 

  34. W. Song and A. Strominger, Warped AdS 3 /dipole-CFT duality, JHEP 05 (2012) 120 [arXiv:1109.0544] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  35. J. Maldacena, D. Martelli and Y. Tachikawa, Comments on string theory backgrounds with non-relativistic conformal symmetry, JHEP 10 (2008) 072 [arXiv:0807.1100] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  36. S.A. Hartnoll and K. Yoshida, Families of IIB duals for nonrelativistic CFTs, JHEP 12 (2008) 071 [arXiv:0810.0298] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  37. A. Donos and J.P. Gauntlett, Supersymmetric solutions for non-relativistic holography, JHEP 03 (2009) 138 [arXiv:0901.0818] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  38. N. Bobev, A. Kundu and K. Pilch, Supersymmetric IIB solutions with Schrödinger symmetry, JHEP 07 (2009) 107 [arXiv:0905.0673] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  39. A. Donos and J.P. Gauntlett, Solutions of type IIB and D = 11 supergravity with Schrödinger(z) symmetry, JHEP 07 (2009) 042 [arXiv:0905.1098] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  40. J. Jeong, H.-C. Kim, S. Lee, E. O Colgain and H. Yavartanoo, Schrödinger invariant solutions of M-theory with enhanced supersymmetry, JHEP 03 (2010) 034 [arXiv:0911.5281] [INSPIRE].

    Article  ADS  Google Scholar 

  41. F. Aprile and J.G. Russo, Models of holographic superconductivity, Phys. Rev. D 81 (2010) 026009 [arXiv:0912.0480] [INSPIRE].

    ADS  Google Scholar 

  42. M. Cvetič, J.T. Liu, H. Lü and C. Pope, Domain wall supergravities from sphere reduction, Nucl. Phys. B 560 (1999) 230 [hep-th/9905096] [INSPIRE].

    Article  ADS  Google Scholar 

  43. N. Bobev and B.C. van Rees, Schrödinger deformations of AdS 3 × S 3, JHEP 08 (2011) 062 [arXiv:1102.2877] [INSPIRE].

    Article  ADS  Google Scholar 

  44. A. Donos and J.P. Gauntlett, Schrödinger invariant solutions of type IIB with enhanced supersymmetry, JHEP 10 (2009) 073 [arXiv:0907.1761] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  45. N. Itzhaki, J.M. Maldacena, J. Sonnenschein and S. Yankielowicz, Supergravity and the large-N limit of theories with sixteen supercharges, Phys. Rev. D 58 (1998) 046004 [hep-th/9802042] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  46. S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a holographic superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].

    Article  ADS  Google Scholar 

  47. F. Denef and S.A. Hartnoll, Landscape of superconducting membranes, Phys. Rev. D 79 (2009) 126008 [arXiv:0901.1160] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  48. S.S. Gubser, C.P. Herzog, S.S. Pufu and T. Tesileanu, Superconductors from superstrings, Phys. Rev. Lett. 103 (2009) 141601 [arXiv:0907.3510] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  49. J.P. Gauntlett, J. Sonner and T. Wiseman, Holographic superconductivity in M-theory, Phys. Rev. Lett. 103 (2009) 151601 [arXiv:0907.3796] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  50. N. Bobev, A. Kundu, K. Pilch and N.P. Warner, Minimal holographic superconductors from maximal supergravity, JHEP 03 (2012) 064 [arXiv:1110.3454] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  51. A. Donos and J.P. Gauntlett, Lifshitz solutions of D = 10 and D = 11 supergravity, JHEP 12 (2010) 002 [arXiv:1008.2062] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  52. D. Cassani and A.F. Faedo, Constructing Lifshitz solutions from AdS, JHEP 05 (2011) 013 [arXiv:1102.5344] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  53. H. Boonstra, K. Skenderis and P. Townsend, The domain wall/QFT correspondence, JHEP 01 (1999) 003 [hep-th/9807137] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  54. N. Ogawa, T. Takayanagi and T. Ugajin, Holographic Fermi surfaces and entanglement entropy, JHEP 01 (2012) 125 [arXiv:1111.1023] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  55. E. Elizalde, M. Lygren and D. Vassilevich, Antisymmetric tensor fields on spheres: functional determinants and nonlocal counterterms, J. Math. Phys. 37 (1996) 3105 [hep-th/9602113] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

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Correspondence to Eric Perlmutter.

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ArXiv ePrint: 1205.0242

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Perlmutter, E. Hyperscaling violation from supergravity. J. High Energ. Phys. 2012, 165 (2012). https://doi.org/10.1007/JHEP06(2012)165

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