Momentum relaxation in holographic massive gravity

TL;DR

This paper investigates how momentum relaxation affects holographic models with massive gravitons, deriving relaxation timescales, analyzing conductivity, and exploring stability, thereby advancing understanding of dissipative effects in holography.

Contribution

It introduces a simple modification to hydrodynamics for momentum relaxation, computes the relaxation timescale, and analyzes conductivity and stability in a holographic massive gravity model.

Findings

Relaxation timescale depends on graviton mass terms.

Zero temperature AC conductivity reduces to Drude form for small masses.

Stability analysis rules out certain spatially modulated instabilities.

Abstract

We study the effects of momentum relaxation on observables in a recently proposed holographic model in which the conservation of momentum in the field theory is broken by the presence of a bulk graviton mass. In the hydrodynamic limit, we show that these effects can be incorporated by a simple modification of the energy-momentum conservation equation to account for the dissipation of momentum over a single characteristic timescale. We compute this timescale as a function of the graviton mass terms and identify the previously known "wall of stability" as the point at which this relaxation timescale becomes negative. We also calculate analytically the zero temperature AC conductivity at low frequencies. In the limit of a small graviton mass this reduces to the simple Drude form, and we compute the corrections to this which are important for larger masses. Finally, we undertake a preliminary investigation of the stability of the zero temperature black brane solution of this model, and rule out spatially modulated instabilities of a certain kind.