Holographic charge transport in Lifshitz black hole backgrounds

TL;DR

This paper investigates charge transport in a holographic Lifshitz black hole background with a UV AdS region, analyzing conductivity and electromagnetic duality, and extending results to higher dimensions.

Contribution

It introduces a detailed study of charge transport in Lifshitz black hole backgrounds with Weyl corrections, including duality relations and extremal conductivity analysis.

Findings

Agreement between membrane paradigm and Kubo's formula for conductivity

Electromagnetic duality relations hold regardless of IR geometry

Conductivity behavior analyzed at extremality and extended to higher dimensions

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.