Abstract
We consider a holographic model consisting of Einstein-Maxwell theory in d + 1 bulk spacetime dimensions with d − 1 massless scalar fields. Momentum relaxation is realised simply through spatially dependent sources for operators dual to the neutral scalars, which can be engineered so that the bulk stress tensor and resulting black brane geometry are homogeneous and isotropic. We analytically calculate the DC conductivity, which is finite. In the d = 3 case, both the black hole geometry and shear-mode currentcurrent correlators are those of a sector of massive gravity.
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References
M. Bianchi, D.Z. Freedman and K. Skenderis, Holographic renormalization, Nucl. Phys. B 631 (2002) 159 [hep-th/0112119] [INSPIRE].
G.T. Horowitz, J.E. Santos and D. Tong, Optical Conductivity with Holographic Lattices, JHEP 07 (2012) 168 [arXiv:1204.0519] [INSPIRE].
G.T. Horowitz, J.E. Santos and D. Tong, Further Evidence for Lattice-Induced Scaling, JHEP 11 (2012) 102 [arXiv:1209.1098] [INSPIRE].
G.T. Horowitz and J.E. Santos, General Relativity and the Cuprates, arXiv:1302.6586 [INSPIRE].
Y. Ling, C. Niu, J.-P. Wu and Z.-Y. Xian, Holographic Lattice in Einstein-Maxwell-Dilaton Gravity, JHEP 11 (2013) 006 [arXiv:1309.4580] [INSPIRE].
P. Chesler, A. Lucas and S. Sachdev, Conformal field theories in a periodic potential: results from holography and field theory, Phys. Rev. D 89 (2014) 026005 [arXiv:1308.0329] [INSPIRE].
A. Ishibashi and K. Maeda, Thermalization of boosted charged AdS black holes by an ionic Lattice, Phys. Rev. D 88 (2013) 066009 [arXiv:1308.5740] [INSPIRE].
S.A. Hartnoll and D.M. Hofman, Locally Critical Resistivities from Umklapp Scattering, Phys. Rev. Lett. 108 (2012) 241601 [arXiv:1201.3917] [INSPIRE].
A. Karch and A. O’Bannon, Metallic AdS/CFT, JHEP 09 (2007) 024 [arXiv:0705.3870] [INSPIRE].
T. Faulkner, N. Iqbal, H. Liu, J. McGreevy and D. Vegh, From Black Holes to Strange Metals, arXiv:1003.1728 [INSPIRE].
S.A. Hartnoll, J. Polchinski, E. Silverstein and D. Tong, Towards strange metallic holography, JHEP 04 (2010) 120 [arXiv:0912.1061] [INSPIRE].
C. de Rham, G. Gabadadze and A.J. Tolley, Resummation of Massive Gravity, Phys. Rev. Lett. 106 (2011) 231101 [arXiv:1011.1232] [INSPIRE].
D. Vegh, Holography without translational symmetry, arXiv:1301.0537 [INSPIRE].
R.A. Davison, Momentum relaxation in holographic massive gravity, Phys. Rev. D 88 (2013) 086003 [arXiv:1306.5792] [INSPIRE].
M. Blake and D. Tong, Universal Resistivity from Holographic Massive Gravity, Phys. Rev. D 88 (2013) 106004 [arXiv:1308.4970] [INSPIRE].
M. Blake, D. Tong and D. Vegh, Holographic Lattices Give the Graviton a Mass, Phys. Rev. Lett. 112 (2014) 071602 [arXiv:1310.3832] [INSPIRE].
A. Donos and S.A. Hartnoll, Interaction-driven localization in holography, Nature Phys. 9 (2013) 649 [arXiv:1212.2998] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic Q-lattices, JHEP 04 (2014) 040 [arXiv:1311.3292] [INSPIRE].
Y. Bardoux, M.M. Caldarelli and C. Charmousis, Shaping black holes with free fields, JHEP 05 (2012) 054 [arXiv:1202.4458] [INSPIRE].
N. Iizuka and K. Maeda, Study of Anisotropic Black Branes in Asymptotically anti-de Sitter, JHEP 07 (2012) 129 [arXiv:1204.3008] [INSPIRE].
D. Mateos and D. Trancanelli, The anisotropic N = 4 super Yang-Mills plasma and its instabilities, Phys. Rev. Lett. 107 (2011) 101601 [arXiv:1105.3472] [INSPIRE].
N. Iqbal and H. Liu, Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm, Phys. Rev. D 79 (2009) 025023 [arXiv:0809.3808] [INSPIRE].
M. Henningson and K. Skenderis, The Holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].
S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [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].
P. Breitenlohner and D.Z. Freedman, Stability in Gauged Extended Supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].
R.A. Davison, K. Schalm and J. Zaanen, Holographic duality and the resistivity of strange metals, arXiv:1311.2451 [INSPIRE].
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Andrade, T., Withers, B. A simple holographic model of momentum relaxation. J. High Energ. Phys. 2014, 101 (2014). https://doi.org/10.1007/JHEP05(2014)101
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DOI: https://doi.org/10.1007/JHEP05(2014)101