Abstract
We study charge transport properties in a domain-wall geometry, whose near horizon IR geometry is a Lifshitz black hole and whose UV geometry is AdS. The action for the gauge field contains the standard Maxwell term plus the Weyl tensor coupled to Maxwell field strengths. In four dimensions we calculate the conductivity via both the membrane paradigm and Kubo’s formula. Precise agreements between both methods are obtained. Moreover, we perform an analysis of the four-dimensional electro-magnetic duality in our domain-wall background and find that the relation between the longitudinal and transverse components of the current-current correlation functions and those of the ‘dual’ counterparts holds, irrespective of the near horizon IR geometry. Conductivity at extremality is also investigated. Generalizations to higher dimensions are performed.
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J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [SPIRES].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [SPIRES].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].
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] [SPIRES].
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [SPIRES].
C.P. Herzog, Lectures on holographic superfluidity and superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [SPIRES].
J. McGreevy, Holographic duality with a view toward many-body physics, Adv. High Energy Phys. 2010 (2010) 723105 [arXiv:0909.0518] [SPIRES].
G.T. Horowitz, Introduction to holographic superconductors, arXiv:1002.1722 [SPIRES].
S. Sachdev, Condensed matter and AdS/CFT, arXiv:1002.2947 [SPIRES].
D.T. Son, Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry, Phys. Rev. D 78 (2008) 046003 [arXiv:0804.3972] [SPIRES].
K. Balasubramanian and J. McGreevy, Gravity duals for non-relativistic CFTs, Phys. Rev. Lett. 101 (2008) 061601 [arXiv:0804.4053] [SPIRES].
S. Kachru, X. Liu and M. Mulligan, Gravity duals of Lifshitz-like fixed points, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725] [SPIRES].
C.P. Herzog, P. Kovtun, S. Sachdev and D.T. Son, Quantum critical transport, duality and M-theory, Phys. Rev. D 75 (2007) 085020 [hep-th/0701036] [SPIRES].
R.C. Myers, S. Sachdev and A. Singh, Holographic quantum critical transport without self-duality, Phys. Rev. D 83 (2011) 066017 [arXiv:1010.0443] [SPIRES].
J.P.S. Lemos, Two-dimensional black holes and planar general relativity, Class. Quant. Grav. 12 (1995) 1081 [gr-qc/9407024] [SPIRES].
J.P.S. Lemos, Cylindrical black hole in general relativity, Phys. Lett. B 353 (1995) 46 [gr-qc/9404041] [SPIRES].
J.P.S. Lemos and V.T. Zanchin, Rotating charged black string and three dimensional black holes, Phys. Rev. D 54 (1996) 3840 [hep-th/9511188] [SPIRES].
M. Taylor, Non-relativistic holography, arXiv:0812.0530 [SPIRES].
U.H. Danielsson and L. Thorlacius, Black holes in asymptotically Lifshitz spacetime, JHEP 03 (2009) 070 [arXiv:0812.5088] [SPIRES].
R.B. Mann, Lifshitz topological black holes, JHEP 06 (2009) 075 [arXiv:0905.1136] [SPIRES].
D.-W. Pang, A note on black holes in asymptotically Lifshitz spacetime, arXiv:0905.2678 [SPIRES].
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] [SPIRES].
G. Bertoldi, B.A. Burrington and A.W. Peet, Thermodynamics of black branes in asymptotically Lifshitz spacetimes, Phys. Rev. D 80 (2009) 126004 [arXiv:0907.4755] [SPIRES].
K. Balasubramanian and J. McGreevy, An analytic Lifshitz black hole, Phys. Rev. D 80 (2009) 104039 [arXiv:0909.0263] [SPIRES].
E. Ayon-Beato, A. Garbarz, G. Giribet and M. Hassaine, Lifshitz black hole in three dimensions, Phys. Rev. D 80 (2009) 104029 [arXiv:0909.1347] [SPIRES].
R.-G. Cai, Y. Liu and Y.-W. Sun, A Lifshitz black hole in four dimensional R 2 gravity, JHEP 10 (2009) 080 [arXiv:0909.2807] [SPIRES].
E. Ayon-Beato, A. Garbarz, G. Giribet and M. Hassaine, Analytic Lifshitz black holes in higher dimensions, JHEP 04 (2010) 030 [arXiv:1001.2361] [SPIRES].
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] [SPIRES].
M. Brigante, H. Liu, R.C. Myers, S. Shenker and S. Yaida, Viscosity bound violation in higher derivative gravity, Phys. Rev. D 77 (2008) 126006 [arXiv:0712.0805] [SPIRES].
A. Ritz and J. Ward, Weyl corrections to holographic conductivity, Phys. Rev. D 79 (2009) 066003 [arXiv:0811.4195] [SPIRES].
P. Kovtun, D.T. Son and A.O. Starinets, Holography and hydrodynamics: Diffusion on stretched horizons, JHEP 10 (2003) 064 [hep-th/0309213] [SPIRES].
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] [SPIRES].
D.T. Son and A.O. Starinets, Minkowski-space correlators in AdS/CFT correspondence: Recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [SPIRES].
S. Caron-Huot, P. Kovtun, G.D. Moore, A. Starinets and L.G. Yaffe, Photon and dilepton production in supersymmetric Yang-Mills plasma, JHEP 12 (2006) 015 [hep-th/0607237] [SPIRES].
A. Nata Atmaja and K. Schalm, Photon and dilepton production in soft wall AdS/QCD, JHEP 08 (2010) 124 [arXiv:0802.1460] [SPIRES].
P. Kovtun and A. Ritz, Universal conductivity and central charges, Phys. Rev. D 78 (2008) 066009 [arXiv:0806.0110] [SPIRES].
D.-W. Pang, Conductivity and diffusion constant in Lifshitz backgrounds, JHEP 01 (2010) 120 [arXiv:0912.2403] [SPIRES].
G.T. Horowitz and M.M. Roberts, Zero temperature limit of holographic superconductors, JHEP 11 (2009) 015 [arXiv:0908.3677] [SPIRES].
K. Goldstein, S. Kachru, S. Prakash and S.P. Trivedi, Holography of charged dilaton black holes, JHEP 08 (2010) 078 [arXiv:0911.3586] [SPIRES].
C.-M. Chen and D.-W. Pang, Holography of charged dilaton black holes in general dimensions, JHEP 06 (2010) 093 [arXiv:1003.5064] [SPIRES].
R.C. Myers, M.F. Paulos and A. Sinha, Holographic hydrodynamics with a chemical potential, JHEP 06 (2009) 006 [arXiv:0903.2834] [SPIRES].
S. Cremonini, K. Hanaki, J.T. Liu and P. Szepietowski, Black holes in five-dimensional gauged supergravity with higher derivatives, JHEP 12 (2009) 045 [arXiv:0812.3572] [SPIRES].
R.-G. Cai and D.-W. Pang, Holography of charged black holes with RF 2 corrections, arXiv:1104.4453 [SPIRES].
M.F. Paulos, Transport coefficients, membrane couplings and universality at extremality, JHEP 02 (2010) 067 [arXiv:0910.4602] [SPIRES].
M. Edalati, J.I. Jottar and R.G. Leigh, Transport coefficients at zero temperature from extremal black holes, JHEP 01 (2010) 018 [arXiv:0910.0645] [SPIRES].
R.-G. Cai, Y. Liu and Y.-W. Sun, Transport coefficients from extremal Gauss-Bonnet black holes, JHEP 04 (2010) 090 [arXiv:0910.4705] [SPIRES].
S.K. Chakrabarti, S. Jain and S. Mukherji, Viscosity to entropy ratio at extremality, JHEP 01 (2010) 068 [arXiv:0910.5132] [SPIRES].
M. Edalati, J.I. Jottar and R.G. Leigh, Shear modes, criticality and extremal black holes, JHEP 04 (2010) 075 [arXiv:1001.0779] [SPIRES].
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Lemos, J.P.S., Pang, DW. Holographic charge transport in Lifshitz black hole backgrounds. J. High Energ. Phys. 2011, 122 (2011). https://doi.org/10.1007/JHEP06(2011)122
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DOI: https://doi.org/10.1007/JHEP06(2011)122