Solid Holography and Massive Gravity

TL;DR

This paper systematically analyzes holographic massive gravity theories, revealing multiple phases that correspond to solid and fluid states, and explores their elastic and electric properties for condensed matter applications.

Contribution

It classifies various phases of holographic massive gravity, distinguishing solids from fluids, and links elastic properties to graviton mass, expanding the scope of models for condensed matter physics.

Findings

Identification of multiple consistent HMG phases as solids or fluids

Derivation of the rigidity modulus from graviton mass

Broader range of electric responses than previously modeled

Abstract

Momentum dissipation is an important ingredient in condensed matter physics that requires a translation breaking sector. In the bottom-up gauge/gravity duality, this implies that the gravity dual is massive. We start here a systematic analysis of holographic massive gravity (HMG) theories, which admit field theory dual interpretations and which, therefore, might store interesting condensed matter applications. We show that there are many phases of HMG that are fully consistent effective field theories and which have been left overlooked in the literature. The most important distinction between the different HMG phases is that they can be clearly separated into solids and fluids. This can be done both at the level of the unbroken spacetime symmetries as well as concerning the elastic properties of the dual materials. We extract the modulus of rigidity of the solid HMG black brane solutions and show how it relates to the graviton mass term. We also consider the implications of the different HMGs on the electric response. We show that the types of response that can be consistently described within this framework is much wider than what is captured by the narrow class of models mostly considered so far.