Holographic Aspects of a Higher Curvature Massive Gravity

Abstract

We study the holographic dual of a massive gravity with Gauss-Bonnet and cubic quasi-topological higher curvature terms. Firstly, we find the energy-momentum two-point function of the 4-dimensional boundary theory where the massive term breaks the conformal symmetry as expected. An $a$-theorem is introduced based on the null energy condition. Then we focus on a black brane solution in this background and derive the ratio of shear viscosity to entropy density for the dual theory. It is worth mentioning that the concept of viscosity as a transport coefficient is obscure in a nontranslational invariant theory as in our case. So although we use the Green-Kubo's formula to derive it, we rather call it the rate of entropy production per the Planckian time due to a strain. Results smoothly cover the massless limit.