Holographic thermal DC response in the hydrodynamic limit

TL;DR

This paper demonstrates how the DC thermal response in holographic models with broken translation symmetry can be described using hydrodynamics, specifically solving linearised Navier-Stokes equations on a torus.

Contribution

It introduces a hydrodynamic framework for calculating DC thermal currents in holographic models with explicit translation symmetry breaking, connecting gravity solutions with fluid dynamics.

Findings

Thermal currents are determined by solving linearised Navier-Stokes equations.

Sub-leading corrections to thermal currents can be systematically computed.

The approach aligns with and extends the fluid-gravity correspondence.

Abstract

We consider black hole solutions of Einstein gravity that describe deformations of CFTs at finite temperature in which spatial translations have been broken explicitly. We focus on deformations that are periodic in the non-compact spatial directions, which effectively corresponds to considering the CFT on a spatial torus with a non-trivial metric. We apply a DC thermal gradient and show that in a hydrodynamic limit the linearised, local thermal currents can be determined by solving linearised, forced Navier-Stokes equations for an incompressible fluid on the torus. We also show how sub-leading corrections to the thermal current can be calculated as well as showing how the full stress tensor response that is generated by the DC source can be obtained. We also compare our results with the fluid-gravity approach.