Abstract
We perform a study of possible instabilities of the infrared AdS 2 × \( {{\mathbb{R}}^2} \) region of solutions to Einstein-Maxwell-dilaton systems which exhibit an intermediate regime of hyperscaling violation and Lifshitz scaling. Focusing on solutions that are magnetically charged, we probe the response of the system to spatially modulated fluctuations, and identify regions of parameter space in which the infrared AdS 2 geometry is unstable to perturbations. The conditions for the existence of instabilities translate to restrictions on the structure of the gauge kinetic function and scalar potential. In turn, these can lead to restrictions on the dynamical critical exponent z and on the amount of hyperscaling violation θ. Our analysis thus provides further evidence for the notion that the true ground state of ‘scaling’ solutions with hyperscaling violation may be spatially modulated phases.
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References
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].
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].
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].
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].
E. Perlmutter, Domain Wall Holography for Finite Temperature Scaling Solutions, JHEP 02 (2011) 013 [arXiv:1006.2124] [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].
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].
N. Ogawa, T. Takayanagi and T. Ugajin, Holographic Fermi Surfaces and Entanglement Entropy, JHEP 01 (2012) 125 [arXiv:1111.1023] [INSPIRE].
S.A. Hartnoll and E. Shaghoulian, Spectral weight in holographic scaling geometries, JHEP 07 (2012) 078 [arXiv:1203.4236] [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].
M. Ammon, M. Kaminski and A. Karch, Hyperscaling-Violation on Probe D-branes, JHEP 11 (2012) 028 [arXiv:1207.1726] [INSPIRE].
J. Sadeghi, B. Pourhassan and A. Asadi, Thermodynamics of string black hole with hyperscaling violation, arXiv:1209.1235 [INSPIRE].
M. Alishahiha, E. O Colgain and H. Yavartanoo, Charged Black Branes with Hyperscaling Violating Factor, JHEP 11 (2012) 137 [arXiv:1209.3946] [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 [arXiv:1209.4047] [INSPIRE].
M. Kulaxizi, A. Parnachev and K. Schalm, On Holographic Entanglement Entropy of Charged Matter, JHEP 10 (2012) 098 [arXiv:1208.2937] [INSPIRE].
A. Adam, B. Crampton, J. Sonner and B. Withers, Bosonic Fractionalisation Transitions, JHEP 01 (2013) 127 [arXiv:1208.3199] [INSPIRE].
M. Alishahiha and H. Yavartanoo, On Holography with Hyperscaling Violation, JHEP 11 (2012) 034 [arXiv:1208.6197] [INSPIRE].
B.S. Kim, Hyperscaling violation: a unified frame for effective holographic theories, JHEP 11 (2012) 061 [arXiv:1210.0540] [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].
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].
A. Donos, J.P. Gauntlett and C. Pantelidou, Semi-local quantum criticality in string/M-theory, JHEP 03 (2013) 103 [arXiv:1212.1462] [INSPIRE].
N. Iizuka 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].
J. Gath, J. Hartong, R. Monteiro and N.A. Obers, Holographic Models for Theories with Hyperscaling Violation, JHEP 04 (2013) 159 [arXiv:1212.3263] [INSPIRE].
S. Harrison, S. Kachru and H. Wang, Resolving Lifshitz Horizons, arXiv:1202.6635 [INSPIRE].
G.T. Horowitz and B. Way, Lifshitz Singularities, Phys. Rev. D 85 (2012) 046008 [arXiv:1111.1243] [INSPIRE].
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].
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].
A. Donos, J.P. Gauntlett and C. Pantelidou, Magnetic and Electric AdS Solutions in String- and M-theory, Class. Quant. Grav. 29 (2012) 194006 [arXiv:1112.4195] [INSPIRE].
A. Donos, J.P. Gauntlett and C. Pantelidou, Spatially modulated instabilities of magnetic black branes, JHEP 01 (2012) 061 [arXiv:1109.0471] [INSPIRE].
M. Rozali, D. Smyth, E. Sorkin and J.B. Stang, Holographic Stripes, Phys. Rev. Lett. 110 (2013) 201603 [arXiv:1211.5600] [INSPIRE].
N. Jokela, M. Jarvinen and M. Lippert, Fluctuations and instabilities of a holographic metal, JHEP 02 (2013) 007 [arXiv:1211.1381] [INSPIRE].
S. Nakamura, H. Ooguri and C.-S. Park, Gravity Dual of Spatially Modulated Phase, Phys. Rev. D 81 (2010) 044018 [arXiv:0911.0679] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic striped phases, JHEP 08 (2011) 140 [arXiv:1106.2004] [INSPIRE].
M. Cvetič et al., Embedding AdS black holes in ten-dimensions and eleven-dimensions, Nucl. Phys. B 558 (1999) 96 [hep-th/9903214] [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].
A. Almuhairi and J. Polchinski, Magnetic AdS × R 2 : Supersymmetry and stability, arXiv:1108.1213 [INSPIRE].
N. Iizuka and K. Maeda, Stripe Instabilities of Geometries with Hyperscaling Violation, Phys. Rev. D 87 (2013) 126006 [arXiv:1301.5677] [INSPIRE].
S. Cremonini, Spatially Modulated Instabilities for Scaling Solutions at Finite Charge Density, arXiv:1310.3279 [INSPIRE].
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ArXiv ePrint: 1212.4172
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Cremonini, S., Sinkovics, A. Spatially modulated instabilities of geometries with hyperscaling violation. J. High Energ. Phys. 2014, 99 (2014). https://doi.org/10.1007/JHEP01(2014)099
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DOI: https://doi.org/10.1007/JHEP01(2014)099