Momentum and charge transport in non-relativistic holographic fluids from Ho\v{r}ava gravity

TL;DR

This paper investigates how momentum and charge diffuse in a non-relativistic holographic fluid modeled by Horava gravity, revealing differences from relativistic cases and proposing modifications to the holographic dictionary.

Contribution

It introduces a modified holographic dictionary for Horava gravity with multiple horizons and different propagation speeds, and computes transport coefficients in this non-relativistic setting.

Findings

Diffusive behavior of momentum and charge confirmed

Diffusion constants and conductivities differ from relativistic theories

Shear viscosity to entropy density ratio is modified

Abstract

We study the linearized transport of transverse momentum and charge in a conjectured field theory dual to a black brane solution of Horava gravity with Lifshitz exponent $z=1$. As expected from general hydrodynamic reasoning, we find that both of these quantities are diffusive over distance and time scales larger than the inverse temperature. We compute the diffusion constants and conductivities of transverse momentum and charge, as well the ratio of shear viscosity to entropy density, and find that they differ from their relativistic counterparts. To derive these results, we propose how the holographic dictionary should be modified to deal with the multiple horizons and differing propagation speeds of bulk excitations in Horava gravity. When possible, as a check on our methods and results, we use the covariant Einstein-Aether formulation of Horava gravity, along with field redefinitions, to re-derive our results from a relativistic bulk theory.