Abstract
We study in detail a variety of gravitational toy models for hyperscaling-violating Lifshitz (hvLif) space-times. These space-times have been recently explored as holographic dual models for condensed matter systems. We start by considering a model of gravity coupled to a massive vector field and a dilaton with a potential. This model supports the full class of hvLif space-times and special attention is given to the particular values of the scaling exponents appearing in certain non-Fermi liquids. We study linearized perturbations in this model, and consider probe fields whose interactions mimic those of the perturbations. The resulting equations of motion for the probe fields are invariant under the Lifshitz scaling. We derive Breitenlohner-Freedman-type bounds for these new probe fields. For the cases of interest the hvLif space-times have curvature invariants that blow up in the UV. We study the problem of constructing models in which the hvLif space-time can have an AdS or Lifshitz UV completion. We also analyze reductions of Schrödinger space-times and reductions of waves on extremal (intersecting) branes, accompanied by transverse space reductions, that are solutions to supergravity-like theories, exploring the allowed parameter range of the hvLif scaling exponents.
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References
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].
C.P. Herzog, Lectures on Holographic Superfluidity and Superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].
J. McGreevy, Holographic duality with a view toward many-body physics, Adv. High Energy Phys. 2010 (2010) 723105 [arXiv:0909.0518] [INSPIRE].
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].
S. Kachru, X. Liu and M. Mulligan, Gravity Duals of Lifshitz-like Fixed Points, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725] [INSPIRE].
M. Taylor, Non-relativistic holography, arXiv:0812.0530 [INSPIRE].
K. Goldstein, S. Kachru, S. Prakash and S.P. Trivedi, Holography of Charged Dilaton Black Holes, JHEP 08 (2010) 078 [arXiv:0911.3586] [INSPIRE].
T. Azeyanagi, W. Li and T. Takayanagi, On String Theory Duals of Lifshitz-like Fixed Points, JHEP 06 (2009) 084 [arXiv:0905.0688] [INSPIRE].
S.A. Hartnoll, J. Polchinski, E. Silverstein and D. Tong, Towards strange metallic holography, JHEP 04 (2010) 120 [arXiv:0912.1061] [INSPIRE].
K. Balasubramanian and K. Narayan, Lifshitz spacetimes from AdS null and cosmological solutions, JHEP 08 (2010) 014 [arXiv:1005.3291] [INSPIRE].
A. Donos and J.P. Gauntlett, Lifshitz Solutions of D = 10 and D = 11 supergravity, JHEP 12 (2010) 002 [arXiv:1008.2062] [INSPIRE].
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].
A. Donos, J.P. Gauntlett, N. Kim and O. Varela, Wrapped M5-branes, consistent truncations and AdS/CMT, JHEP 12 (2010) 003 [arXiv:1009.3805] [INSPIRE].
D. Cassani and A.F. Faedo, Constructing Lifshitz solutions from AdS, JHEP 05 (2011) 013 [arXiv:1102.5344] [INSPIRE].
N. Halmagyi, M. Petrini and A. Zaffaroni, Non-Relativistic Solutions of N = 2 Gauged Supergravity, JHEP 08 (2011) 041 [arXiv:1102.5740] [INSPIRE].
K. Narayan, Lifshitz-like systems and AdS null deformations, Phys. Rev. D 84 (2011) 086001 [arXiv:1103.1279] [INSPIRE].
W. Chemissany and J. Hartong, From D3-branes to Lifshitz Space-Times, Class. Quant. Grav. 28 (2011) 195011 [arXiv:1105.0612] [INSPIRE].
D.S. Fisher, Scaling and critical slowing down in random-field Ising systems, Phys. Rev. Lett. 56 (1986) 416 [INSPIRE].
N. Ogawa, T. Takayanagi and T. Ugajin, Holographic Fermi Surfaces and Entanglement Entropy, JHEP 01 (2012) 125 [arXiv:1111.1023] [INSPIRE].
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].
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].
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].
B. Gouteraux and E. Kiritsis, Generalized Holographic Quantum Criticality at Finite Density, JHEP 12 (2011) 036 [arXiv:1107.2116] [INSPIRE].
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].
H. Singh, Special limits and non-relativistic solutions, JHEP 12 (2010) 061 [arXiv:1009.0651] [INSPIRE].
K. Narayan, On Lifshitz scaling and hyperscaling violation in string theory, Phys. Rev. D 85 (2012) 106006 [arXiv:1202.5935] [INSPIRE].
H. Singh, Lifshitz/Schródinger Dp-branes and dynamical exponents, JHEP 07 (2012) 082 [arXiv:1202.6533] [INSPIRE].
P. Dey and S. Roy, Lifshitz-like space-time from intersecting branes in string/M theory, JHEP 06 (2012) 129 [arXiv:1203.5381] [INSPIRE].
P. Dey and S. Roy, Intersecting D-branes and Lifshitz-like space-time, Phys. Rev. D 86 (2012) 066009 [arXiv:1204.4858] [INSPIRE].
C. Charmousis, B. Gouteraux and E. Kiritsis, Higher-derivative scalar-vector-tensor theories: black holes, Galileons, singularity cloaking and holography, JHEP 09 (2012) 011 [arXiv:1206.1499] [INSPIRE].
M. Ammon, M. Kaminski and A. Karch, Hyperscaling-Violation on Probe D-branes, JHEP 11 (2012) 028 [arXiv:1207.1726] [INSPIRE].
J. Bhattacharya, S. Cremonini and A. Sinkovics, On the IR completion of geometries with hyperscaling violation, JHEP 02 (2013) 147 [arXiv:1208.1752] [INSPIRE].
N. Kundu, P. Narayan, N. Sircar and S.P. Trivedi, Entangled Dilaton Dyons, JHEP JHEP03 (2013) 155 [arXiv:1208.2008] [INSPIRE].
P. Dey and S. Roy, Lifshitz metric with hyperscaling violation from NS5-Dp states in string theory, Phys. Lett. B 720 (2013) 419 [arXiv:1209.1049] [INSPIRE].
P. Bueno, W. Chemissany, P. Meessen, T. Ortín and C. Shahbazi, Lifshitz-like Solutions with Hyperscaling Violation in Ungauged Supergravity, JHEP 01 (2013) 189 .
E. Shaghoulian, Holographic Entanglement Entropy and Fermi Surfaces, JHEP 05 (2012) 065 [arXiv:1112.2702] [INSPIRE].
S.A. Hartnoll and E. Shaghoulian, Spectral weight in holographic scaling geometries, JHEP 07 (2012) 078 [arXiv:1203.4236] [INSPIRE].
T. Takayanagi, Entanglement Entropy from a Holographic Viewpoint, Class. Quant. Grav. 29 (2012) 153001 [arXiv:1204.2450] [INSPIRE].
P. Dey and S. Roy, Holographic entanglement entropy of the near horizon 1/4 BPS F-Dp bound states, arXiv:1208.1820 [INSPIRE].
M. Kulaxizi, A. Parnachev and K. Schalm, On Holographic Entanglement Entropy of Charged Matter, JHEP 10 (2012) 098 [arXiv:1208.2937] [INSPIRE].
M. Alishahiha and H. Yavartanoo, On Holography with Hyperscaling Violation, JHEP 11 (2012) 034 [arXiv:1208.6197] [INSPIRE].
M. Edalati, J.F. Pedraza and W. Tangarife Garcia, Quantum Fluctuations in Holographic Theories with Hyperscaling Violation, Phys. Rev. D 87 (2013) 046001 [arXiv:1210.6993] [INSPIRE].
K. Copsey and R. Mann, Pathologies in Asymptotically Lifshitz Spacetimes, JHEP 03 (2011) 039 [arXiv:1011.3502] [INSPIRE].
G.T. Horowitz and B. Way, Lifshitz Singularities, Phys. Rev. D 85 (2012) 046008 [arXiv:1111.1243] [INSPIRE].
K. Copsey and R. Mann, Singularities in Hyperscaling Violating Spacetimes, arXiv:1210.1231 [INSPIRE].
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].
S. Harrison, S. Kachru and H. Wang, Resolving Lifshitz Horizons, arXiv:1202.6635 [INSPIRE].
E. Kiritsis, Lorentz violation, Gravity, Dissipation and Holography, JHEP 01 (2013) 030 [arXiv:1207.2325] [INSPIRE].
N. Iizuka, S. Kachru, N. Kundu, P. Narayan, N. Sircar et al., Extremal Horizons with Reduced Symmetry: Hyperscaling Violation, Stripes and a Classification for the Homogeneous Case, JHEP 03 (2013) 126 [arXiv:1212.1948] [INSPIRE].
B. Gouteraux and E. Kiritsis, Quantum critical lines in holographic phases with (un)broken symmetry, JHEP 04 (2013) 053 [arXiv:1212.2625] [INSPIRE].
W. Chemissany, D. Geissbuhler, J. Hartong and B. Rollier, Holographic Renormalization for z=2 Lifshitz Space-Times from AdS, Class. Quant. Grav. 29 (2012) 235017 [arXiv:1205.5777] [INSPIRE].
B.S. Kim, Schródinger Holography with and without Hyperscaling Violation, JHEP 06 (2012) 116 [arXiv:1202.6062] [INSPIRE].
E. Perlmutter, Hyperscaling violation from supergravity, JHEP 06 (2012) 165 [arXiv:1205.0242] [INSPIRE].
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].
R. Argurio, Brane physics in M-theory, hep-th/9807171 [INSPIRE].
G. Gibbons and K.-i. Maeda, Black Holes and Membranes in Higher Dimensional Theories with Dilaton Fields, Nucl. Phys. B 298 (1988) 741 [INSPIRE].
M.M. Caldarelli, R. Emparan and B. Van Pol, Higher-dimensional Rotating Charged Black Holes, JHEP 04 (2011) 013 [arXiv:1012.4517] [INSPIRE].
U.H. Danielsson and L. Thorlacius, Black holes in asymptotically Lifshitz spacetime, JHEP 03 (2009) 070 [arXiv:0812.5088] [INSPIRE].
G. Bertoldi, B.A. Burrington and A. Peet, Black Holes in asymptotically Lifshitz spacetimes with arbitrary critical exponent, Phys. Rev. D 80 (2009) 126003 [arXiv:0905.3183] [INSPIRE].
K. Balasubramanian and J. McGreevy, An Analytic Lifshitz black hole, Phys. Rev. D 80 (2009) 104039 [arXiv:0909.0263] [INSPIRE].
J. Tarrio and S. Vandoren, Black holes and black branes in Lifshitz spacetimes, JHEP 09 (2011) 017 [arXiv:1105.6335] [INSPIRE].
J. Sadeghi, B. Pourhasan and F. Pourasadollah, Thermodynamics of Schrdinger black holes with hyperscaling violation, Phys. Lett. B 720 (2013) 244 [arXiv:1209.1874] [INSPIRE].
M. Alishahiha, E. O Colgain and H. Yavartanoo, Charged Black Branes with Hyperscaling Violating Factor, JHEP 11 (2012) 137 [arXiv:1209.3946] [INSPIRE].
A. Donos, J.P. Gauntlett, J. Sonner and B. Withers, Competing orders in M-theory: superfluids, stripes and metamagnetism, JHEP 03 (2013) 108 [arXiv:1212.0871] [INSPIRE].
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].
S. Barisch-Dick, G. Lopes Cardoso, M. Haack and S. Nampuri, Extremal black brane solutions in five-dimensional gauged supergravity, JHEP 02 (2013) 103 [arXiv:1211.0832] [INSPIRE].
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Gath, J., Hartong, J., Monteiro, R. et al. Holographic models for theories with hyperscaling violation. J. High Energ. Phys. 2013, 159 (2013). https://doi.org/10.1007/JHEP04(2013)159
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DOI: https://doi.org/10.1007/JHEP04(2013)159