Counterterms in Massive Gravity Theory

TL;DR

This paper derives local boundary counterterms for four-dimensional massive gravity with a negative cosmological constant and analyzes the boundary field theory properties within the AdS/CFT framework, including stress tensor conservation and thermodynamics.

Contribution

It provides the first derivation of local boundary counterterms in massive gravity and applies them to study boundary stress tensor and thermodynamics in AdS/CFT.

Findings

Boundary stress tensor is conserved.

Momentum dissipation occurs at linear response.

Thermodynamic quantities match literature results up to finite counterterms.

Abstract

We derived local boundary counterterms in massive gravity theory with a negative cosmological constant in four dimensions. With these counterterms at hand we analyzed the properties of the boundary field theory in the context of AdS/CFT duality by calculating the boundary stress energy tensor. The calculation shows that the boundary stress energy tensor is conserved, and momentum dissipation might occur on the level of linear response only. We also calculated the thermodynamic quantities and the boundary stress energy tensor for a specific type of solutions. The thermodynamic potentials agree with the results of literature up to some constants which can be removed by adding finite counterterms.