DC Conductivity and Higher Derivative Gravity

TL;DR

This paper explores how to compute DC conductivity in higher derivative gravity theories using holography, linking horizon fluid dynamics to boundary transport properties.

Contribution

It introduces a method to derive DC conductivity from Stokes equations on black hole horizons in higher derivative gravity models.

Findings

DC conductivity can be obtained from horizon fluid equations.

Horizon fluxes determine boundary DC transport currents.

Method applies to Gauss-Bonnet and more general higher derivative theories.

Abstract

For Gauss-Bonnet gravity and in the context of holography we show how the thermal DC conductivity can be obtained by solving a generalised system of Stokes equations for an auxiliary fluid on a curved black hole horizon. For more general higher derivative theories of gravity coupled to gauge-fields, we also analyse the linearised thermal and electric currents that are produced by DC thermal and electric sources. We show how suitably defined DC transport current fluxes of the dual field theory are given by current fluxes defined at the black horizon.