Holographic charge transport in Lifshitz black hole backgrounds

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.

22 pages, typos corrected

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• Higher-Derivative Gravity with Non-minimally Coupled Maxwell Field
• Thermodynamics and gauge/gravity duality for Lifshitz black holes in the presence of exponential electrodynamics
• Holographic charge transport in 2+1 dimensions at finite $N$
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• Holographic charge diffusion in non relativistic branes
• Lifshitz black holes in four-dimensional Critical Gravity
• Effective Lifshitz black holes, hydrodynamics, and transport coefficients in fluid/gravity correspondence