DC Conductivity of Magnetised Holographic Matter

TL;DR

This paper derives a method to compute the DC conductivity of magnetised holographic matter using horizon data from black hole solutions, applicable to various lattice models.

Contribution

It introduces a general approach to calculate thermoelectric DC conductivity via solving Stokes equations on black hole horizons in Einstein-Maxwell-scalar theories.

Findings

Explicit solutions for Stokes equations in Q-lattice models

Expressions for DC conductivity in terms of horizon data

Demonstration of method's applicability to different lattice structures

Abstract

We consider general black hole solutions of Einstein-Maxwell-scalar theory that are holographically dual to conformal field theories at finite charge density with non-vanishing magnetic fields and local magnetisation currents, which generically break translation invariance explicitly. We show that the thermoelectric DC conductivity of the field theory can be obtained by solving a system of generalised Stokes equations on the black hole horizon. For various examples, including Q-lattices and one-dimensional lattices, we solve the Stokes equations explicitly and obtain expressions for the DC conductivity in terms of the solution at the black hole horizon.