Universal Resistivity from Holographic Massive Gravity

TL;DR

The paper addresses momentum dissipation in holography by using ghost-free holographic massive gravity to derive a universal DC conductivity that depends only on horizon data. Employing a membrane-paradigm analysis, it identifies a massless bulk mode and obtains the analytic form $\sigma_{DC} = \frac{1}{e^2}\left(1 + \frac{4 e^4 {\cal Q}^2}{\gamma^2}\frac{r_h^2}{m^2(r_h)}\right)$, linking transport to horizon quantities $r_h$ and $m^2(r_h)$; this result remains valid under dilaton coupling, becoming $\sigma_{DC} = \frac{1}{e^2}\left( Z(\phi(r_h)) + \frac{4 e^4 {\cal Q}^2}{\gamma^2}\frac{r_h^2}{m^2(r_h)} \right)$. The conductivity ties to a hydrodynamic scattering time $\tau^{-1} = \frac{\gamma^2}{4 e^2 r_h^2}\frac{m^2(r_h)}{{\cal E}+P}$, consistent with momentum-relaxation physics, and the paper also demonstrates sensible black-hole thermodynamics via finite counterterms. Overall, the work provides analytic, horizon-driven DC transport in momentum-dissipating holographic theories and discusses the scope and limitations of this universality for broader gravitational models.

Abstract

Massive gravity provides a holographic model for theories exhibiting momentum dissipation. We provide an analytic expression for the DC conductivity. The result is universal, depending only on properties of the infra-red horizon, and holds at finite temperature and charge density. In addition, we provide a derivation of black hole thermodynamics in holographic massive gravity and show that the resulting physics is sensible.