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Schrödinger holography with and without hyperscaling violation

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Abstract

We study the properties of the Schrödinger-type non-relativistic holography for general dynamical exponent z with and without hyperscaling violation exponent θ. The scalar correlation function has a more general form due to general z as well as the presence of θ, whose effects also modify the scaling dimension of the scalar operator. We propose a prescription for minimal surfaces of this “codimension 2 holography”, and demonstrate the (d − 1) dimensional area law for the entanglement entropy from (d + 3) dimensional Schrödinger backgrounds. Surprisingly, the area law is violated for d + 1 < z < d + 2, even without hyperscaling violation, which interpolates between the logarithmic violation and extensive volume dependence of entanglement entropy. Similar violations are also found in the presence of the hyperscaling violation. Their dual field theories are expected to have novel phases for the parameter range, including Fermi surface. We also analyze string theory embeddings using non-relativistic branes.

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References

  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].

    MathSciNet  ADS  MATH  Google Scholar 

  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].

    Article  MathSciNet  ADS  Google Scholar 

  3. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].

    MathSciNet  ADS  MATH  Google Scholar 

  4. O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  5. 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 

  6. 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 

  7. W.D. Goldberger, AdS/CFT duality for non-relativistic field theory, JHEP 03 (2009) 069 [arXiv:0806.2867] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. J.L. Barbon and C.A. Fuertes, On the spectrum of nonrelativistic AdS/CFT, JHEP 09 (2008)030 [arXiv:0806.3244] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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

  11. 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 

  12. 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 

  13. 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 

  14. 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].

    Article  ADS  Google Scholar 

  15. D. Nickel and D.T. Son, Deconstructing holographic liquids, New J. Phys. 13 (2011) 075010 [arXiv:1009.3094] [INSPIRE].

    Article  ADS  Google Scholar 

  16. I. Heemskerk and J. Polchinski, Holographic and Wilsonian Renormalization Groups, JHEP 06 (2011) 031 [arXiv:1010.1264] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  17. T. Faulkner, H. Liu and M. Rangamani, Integrating out geometry: Holographic Wilsonian RG and the membrane paradigm, JHEP 08 (2011) 051 [arXiv:1010.4036] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  18. 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].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. 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].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. 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].

    Article  ADS  Google Scholar 

  21. B. Gouteraux and E. Kiritsis, Generalized Holographic Quantum Criticality at Finite Density, JHEP 12 (2011) 036 [arXiv:1107.2116] [INSPIRE].

    Article  ADS  Google Scholar 

  22. 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 

  23. K. Goldstein, S. Kachru, S. Prakash and S.P. Trivedi, Holography of Charged Dilaton Black Holes, JHEP 08 (2010) 078 [arXiv:0911.3586] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. 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].

    Article  MathSciNet  ADS  Google Scholar 

  25. E. Perlmutter, Domain Wall Holography for Finite Temperature Scaling Solutions, JHEP 02 (2011) 013 [arXiv:1006.2124] [INSPIRE].

    ADS  Google Scholar 

  26. 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].

    ADS  Google Scholar 

  27. 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].

    ADS  Google Scholar 

  28. M. Cadoni and P. Pani, Holography of charged dilatonic black branes at finite temperature, JHEP 04 (2011) 049 [arXiv:1102.3820] [INSPIRE].

    Article  ADS  Google Scholar 

  29. 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].

    Article  ADS  Google Scholar 

  30. P. Berglund, J. Bhattacharyya and D. Mattingly, Charged Dilatonic AdS Black Branes in Arbitrary Dimensions, arXiv:1107.3096 [INSPIRE].

  31. 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 

  32. S. Harrison, S. Kachru and H. Wang, Resolving Lifshitz Horizons, arXiv:1202.6635 [INSPIRE].

  33. S. Sachdev, Quantum Phase Transitions, 2nd ed., Cambridge University Press, Cambridge, U.K. (2011).

    Book  MATH  Google Scholar 

  34. D.S. Fisher, Scaling and critical slowing down in random-field Ising systems, Phys. Rev. Lett. 56 (1986) 416 [INSPIRE].

    Article  ADS  Google Scholar 

  35. 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].

    ADS  Google Scholar 

  36. H. Liu, J. McGreevy and D. Vegh, Non-Fermi liquids from holography, Phys. Rev. D 83 (2011)065029 [arXiv:0903.2477] [INSPIRE].

    ADS  Google Scholar 

  37. 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].

    Article  MathSciNet  ADS  Google Scholar 

  38. 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].

    ADS  Google Scholar 

  39. S.A. Hartnoll, D.M. Hofman and A. Tavanfar, Holographically smeared Fermi surface: Quantum oscillations and Luttinger count in electron stars, Europhys. Lett. 95 (2011) 31002 [arXiv:1011.2502] [INSPIRE].

    Article  ADS  Google Scholar 

  40. S.A. Hartnoll, D.M. Hofman and D. Vegh, Stellar spectroscopy: Fermions and holographic Lifshitz criticality, JHEP 08 (2011) 096 [arXiv:1105.3197] [INSPIRE].

    Article  ADS  Google Scholar 

  41. N. Iqbal, H. Liu and M. Mezei, Semi-local quantum liquids, JHEP 04 (2012) 086 [arXiv:1105.4621] [INSPIRE].

    Article  ADS  Google Scholar 

  42. S. Sachdev, A model of a Fermi liquid using gauge-gravity duality, Phys. Rev. D 84 (2011) 066009 [arXiv:1107.5321] [INSPIRE].

    ADS  Google Scholar 

  43. A. Allais, J. McGreevy and S.J. Suh, A quantum electron star, arXiv:1202.5308 [INSPIRE].

  44. S.A. Hartnoll, J. Polchinski, E. Silverstein and D. Tong, Towards strange metallic holography, JHEP 04 (2010) 120 [arXiv:0912.1061] [INSPIRE].

    Article  ADS  Google Scholar 

  45. S.A. Hartnoll and A. Tavanfar, Electron stars for holographic metallic criticality, Phys. Rev. D 83 (2011) 046003 [arXiv:1008.2828] [INSPIRE].

    ADS  Google Scholar 

  46. S. Sachdev, Holographic metals and the fractionalized Fermi liquid, Phys. Rev. Lett. 105 (2010)151602 [arXiv:1006.3794] [INSPIRE].

    Article  ADS  Google Scholar 

  47. L. Huijse and S. Sachdev, Fermi surfaces and gauge-gravity duality, Phys. Rev. D 84 (2011) 026001 [arXiv:1104.5022] [INSPIRE].

    ADS  Google Scholar 

  48. S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  49. S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  50. T. Nishioka, S. Ryu and T. Takayanagi, Holographic Entanglement Entropy: An Overview, J. Phys. A 42 (2009) 504008 [arXiv:0905.0932] [INSPIRE].

    MathSciNet  Google Scholar 

  51. J. Eisert, M. Cramer and M. Plenio, Area laws for the entanglement entropy - a review, Rev. Mod. Phys. 82 (2010) 277 [arXiv:0808.3773] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  52. M.M. Wolf, Violation of the entropic area law for Fermions, Phys. Rev. Lett. 96 (2006) 010404 [quant-ph/0503219] [INSPIRE].

    Article  ADS  Google Scholar 

  53. D. Gioev and I. Klich, Entanglement Entropy of Fermions in Any Dimension and the Widom Conjecture, Phys. Rev. Lett. 96 (2006) 100503 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  54. B. Swingle, Entanglement Entropy and the Fermi Surface, arXiv:0908.1724 [INSPIRE].

  55. B. Swingle, Conformal Field Theory on the Fermi Surface, arXiv:1002.4635 [INSPIRE].

  56. Y. Zhang, T. Grover and A. Vishwanath, Entanglement Entropy of Critical Spin Liquids, Physical Review Letters 107 (2011), no. 6 067202 [arXiv:1102.0350].

    Google Scholar 

  57. L. Huijse and B. Swingle, Area law violations in a supersymmetric model, arXiv:1202.2367 [INSPIRE].

  58. E. Shaghoulian, Holographic Entanglement Entropy and Fermi Surfaces, JHEP 05 (2012) 065 [arXiv:1112.2702] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  59. N. Iqbal and H. Liu, Luttinger’s Theorem, Superfluid Vortices and Holography, arXiv:1112.3671 [INSPIRE].

  60. H. Liu and M. Mezei, A Refinement of entanglement entropy and the number of degrees of freedom, arXiv:1202.2070 [INSPIRE].

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

    Article  MathSciNet  ADS  Google Scholar 

  62. M. Alishahiha, Y. Oz and J.G. Russo, Supergravity and light - like noncommutativity, JHEP 09 (2000) 002 [hep-th/0007215] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  63. V.E. Hubeny, M. Rangamani and S.F. Ross, Causal structures and holography, JHEP 07 (2005)037 [hep-th/0504034] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  64. M. Alishahiha and O.J. Ganor, Twisted backgrounds, PP waves and nonlocal field theories, JHEP 03 (2003) 006 [hep-th/0301080] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  65. E.G. Gimon, A. Hashimoto, V.E. Hubeny, O. Lunin and M. Rangamani, Black strings in asymptotically plane wave geometries, JHEP 08 (2003) 035 [hep-th/0306131] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  66. C.P. Herzog, M. Rangamani and S.F. Ross, Heating up Galilean holography, JHEP 11 (2008)080 [arXiv:0807.1099] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  67. A. Adams, K. Balasubramanian and J. McGreevy, Hot Spacetimes for Cold Atoms, JHEP 11 (2008)059 [arXiv:0807.1111] [INSPIRE].

    Article  ADS  Google Scholar 

  68. D. Yamada, Thermodynamics of Black Holes in Schrödinger Space, Class. Quant. Grav. 26 (2009)075006 [arXiv:0809.4928] [INSPIRE].

    Article  ADS  Google Scholar 

  69. M. Ammon, C. Hoyos, A. O’Bannon and J.M. Wu, Holographic Flavor Transport in Schrödinger Spacetime, JHEP 06 (2010) 012 [arXiv:1003.5913] [INSPIRE].

    Article  ADS  Google Scholar 

  70. 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 

  71. B.S. Kim and D. Yamada, Properties of Schroedinger Black Holes from AdS Space, JHEP 07 (2011) 120 [arXiv:1008.3286] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  72. B.S. Kim, E. Kiritsis and C. Panagopoulos, Holographic quantum criticality and strange metal transport, New J. Phys. 14 (2012) 043045 [arXiv:1012.3464] [INSPIRE].

    Article  ADS  Google Scholar 

  73. S.S. Gubser, Curvature singularities: The Good, the bad and the naked, Adv. Theor. Math. Phys. 4 (2000) 679 [hep-th/0002160] [INSPIRE].

    MathSciNet  MATH  Google Scholar 

  74. S. Hyun, J. Jeong and B.S. Kim, Finite Temperature Aging Holography, JHEP 03 (2012) 010 [arXiv:1108.5549] [INSPIRE].

    Article  ADS  Google Scholar 

  75. 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 

  76. K. Balasubramanian and J. McGreevy, The Particle number in Galilean holography, JHEP 01 (2011) 137 [arXiv:1007.2184] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  77. C. Hoyos and P. Koroteev, On the Null Energy Condition and Causality in Lifshitz Holography, Phys. Rev. D 82 (2010) 084002 [Erratum ibid. D 82 (2010) 109905] [arXiv:1007.1428] [INSPIRE].

    ADS  Google Scholar 

  78. E. Perlmutter, Hyperscaling violation from supergravity, arXiv:1205.0242 [INSPIRE].

  79. J.D. Brown and J.W. York, Quasilocal energy and conserved charges derived from the gravitational action, Phys. Rev. D 47 (1993) 1407 [gr-qc/9209012] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  80. V. Balasubramanian and P. Kraus, A Stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  81. C.A. Fuertes and S. Moroz, Correlation functions in the non-relativistic AdS/CFT correspondence, Phys. Rev. D 79 (2009) 106004 [arXiv:0903.1844] [INSPIRE].

    ADS  Google Scholar 

  82. A. Volovich and C. Wen, Correlation Functions in Non-Relativistic Holography, JHEP 05 (2009)087 [arXiv:0903.2455] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  83. R.G. Leigh and N.N. Hoang, Real-Time Correlators and Non-Relativistic Holography, JHEP 11 (2009)010 [arXiv:0904.4270] [INSPIRE].

    Article  ADS  Google Scholar 

  84. E. Barnes, D. Vaman and C. Wu, Holographic real-time non-relativistic correlators at zero and finite temperature, Phys. Rev. D 82 (2010) 125042 [arXiv:1007.1644] [INSPIRE].

    ADS  Google Scholar 

  85. D.T. Son and A.O. Starinets, Minkowski space correlators in AdS/CFT correspondence: Recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  86. D.T. Son and A.O. Starinets, Viscosity, Black Holes and Quantum Field Theory, Ann. Rev. Nucl. Part. Sci. 57 (2007) 95 [arXiv:0704.0240] [INSPIRE].

    Article  ADS  Google Scholar 

  87. 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 

  88. 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 

  89. V.E. Hubeny, M. Rangamani and T. Takayanagi, A Covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  90. 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 

  91. A. Adams, A. Maloney, A. Sinha and S.E. Vazquez, 1/N Effects in Non-Relativistic Gauge-Gravity Duality, JHEP 03 (2009) 097 [arXiv:0812.0166] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  92. J.P. Gauntlett, S. Kim, O. Varela and D. Waldram, Consistent supersymmetric Kaluza-Klein truncations with massive modes, JHEP 04 (2009) 102 [arXiv:0901.0676] [INSPIRE].

    Article  ADS  Google Scholar 

  93. 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 

  94. S.S. Pal, Non-relativistic supersymmetric Dp-branes, Class. Quant. Grav. 26 (2009) 245014 [arXiv:0904.3620] [INSPIRE].

    Article  ADS  Google Scholar 

  95. 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 

  96. 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 

  97. E. O Colgain, O. Varela and H. Yavartanoo, Non-relativistic M-theory solutions based on Kähler-Einstein spaces, JHEP 07 (2009) 081 [arXiv:0906.0261] [INSPIRE].

    Article  ADS  Google Scholar 

  98. 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 

  99. A. Bergman and O.J. Ganor, Dipoles, twists and noncommutative gauge theory, JHEP 10 (2000)018 [hep-th/0008030] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  100. A. Bergman, K. Dasgupta, O.J. Ganor, J.L. Karczmarek and G. Rajesh, Nonlocal field theories and their gravity duals, Phys. Rev. D 65 (2002) 066005 [hep-th/0103090] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  101. O.J. Ganor, A. Hashimoto, S. Jue, B.S. Kim and A. Ndirango, Aspects of Puff Field Theory, JHEP 08 (2007) 035 [hep-th/0702030] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  102. J.L. Barbon and C.A. Fuertes, Holographic entanglement entropy probes (non)locality, JHEP 04 (2008) 096 [arXiv:0803.1928] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  103. B.S. Kim, work in progress.

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

    ADS  Google Scholar 

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

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  1. Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, 69978, Tel Aviv, Israel

    Bom Soo Kim

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Kim, B.S. Schrödinger holography with and without hyperscaling violation. J. High Energ. Phys. 2012, 116 (2012). https://doi.org/10.1007/JHEP06(2012)116

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