Momentum relaxation from the fluid/gravity correspondence

TL;DR

This work develops a hydrodynamic description of a holographic theory with momentum relaxation by applying the fluid/gravity correspondence to a 5D Einstein–Maxwell–Scalar bulk with translational symmetry broken by linear scalar sources. It derives constitutive relations for the boundary current and stress tensor, plus the scalar sector, in a derivative expansion, highlighting scalar-induced corrections beyond leading order and their impact on transport. In linear response, the authors obtain exact horizon-data expressions for DC thermoelectric conductivities and unveil a low-frequency AC response comprising a coherent Drude-like piece and an incoherent constant piece, with the Ward identity for momentum relaxation playing a central role. The results provide a coherent, first-principles hydrodynamic framework for momentum-relaxing holographic transport and offer a platform to explore diffusive, magnetotransport, and inhomogeneous-lattice phenomena in strongly coupled systems.

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.