Thermoelectric DC conductivities and Stokes flows on black hole horizons

TL;DR

This paper links thermoelectric DC conductivities in holographic models to Stokes flow equations on black hole horizons, providing explicit formulas for various lattice configurations.

Contribution

It introduces a novel approach connecting horizon fluid dynamics to DC conductivities in Einstein-Maxwell-scalar theories with broken translation invariance.

Findings

Derived closed-form expressions for DC conductivity in Q-lattices.

Solved fluid equations for one-dimensional lattices.

Obtained perturbative leading order DC conductivity for near-translationally invariant lattices.

Abstract

We consider a general class of electrically charged black holes of Einstein-Maxwell-scalar theory that are holographically dual to conformal field theories at finite charge density which break translation invariance explicitly. We examine the linearised perturbations about the solutions that are associated with the thermoelectric DC conductivity. We show that there is a decoupled sector at the black hole horizon which must solve generalised Stokes equations for a charged fluid. By solving these equations we can obtain the DC conductivity of the dual field theory. For Q-lattices and one-dimensional lattices we solve the fluid equations to obtain closed form expressions for the DC conductivity in terms of the solution at the black hole horizon. We also determine the leading order DC conductivity for lattices that can be expanded as a perturbative series about translationally invariant solutions.