Momentum relaxation from the fluid/gravity correspondence

TL;DR

This paper develops a hydrodynamical framework using fluid/gravity correspondence to describe momentum relaxation in holographic theories with broken translation invariance, providing new insights into transport properties.

Contribution

It systematically derives constitutive relations and Ward identities for momentum relaxation beyond leading order, improving upon previous models.

Findings

Derived low-frequency thermoelectric transport coefficients.

Established a hydrodynamical description for momentum relaxation.

Identified differences from prior models at higher order.

Abstract

We provide a hydrodynamical description of a holographic theory with broken translation invariance. We use the fluid/gravity correspondence to systematically obtain both the constitutive relations for the currents and the Ward identity for momentum relaxation in a derivative expansion. Beyond leading order in the strength of momentum relaxation, our results differ from a model previously proposed by Hartnoll et al. As an application of these techniques we consider charge and heat transport in the boundary theory. We derive the low frequency thermoelectric transport coefficients of the holographic theory from the linearised hydrodynamics.