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.

Highlights

  • On the other hand, several studies have been performed for decades to generalize the graviton field to a massive one with different motivations from theoretical curiosity to phenomenological model buildings

  • A fundamental higher derivative gravity is expected to be derived from a string theory calculation, the Gauss–Bonnet and cubic quasitopological higher curvature gravities may be considered as toy models with rich structure to investigate the dual quantum field theory on the boundary [7,8,9]

  • The existence of a dual theory to the Gauss–Bonnet gravity is under question [26,27], we merely considered it as a toy model

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Summary

Introduction

Several studies have been performed for decades to generalize the graviton field to a massive one with different motivations from theoretical curiosity to phenomenological model buildings (for a recent review see [10]). The Gauss–Bonnet gravity is widely discussed in holographic literature at least as a toy model or theoretical laboratory to study general aspects of quantum field theories or CFT’s. In this direction, one may consider the addition of massive gravity as a relevant perturbation of conformal symmetry. [37] has different interpretation for the bound and argues that it is expected to exist due to a basic quantum mechanical uncertainty We apply this interpretation and take η as the rate of entropy production and extend the calculation to include higher curvature theories with mass term. We consider the unitarity and causality bounds on the boundary theory

Quasi-topological massive gravity and holography
Holographic picture on the boundary
The a-theorem
L2 gμν
Quasi-topological black brane in Gauss–Bonnet massive gravity
The black brane solution
L2 δi j
The rate of entropy production
Physical constraints
Conclusion

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