Holographic Renormalization and Stress Tensors in New Massive Gravity

TL;DR

This paper develops holographic renormalization techniques for new massive gravity in three dimensions, computing boundary stress tensors, correlators, and physical quantities like central charges and black hole parameters, revealing aspects of higher curvature gravity.

Contribution

It introduces a method to holographically renormalize boundary stress tensors in new massive gravity using Fefferman-Graham coordinates, including counter terms and correlator calculations.

Findings

Computed holographically renormalized stress tensors and correlators.

Determined central charges, mass, and angular momentum of AdS black holes.

Revealed aspects of higher curvature gravity through Fefferman-Graham expansion.

Abstract

We obtain holographically renormalized boundary stress tensors with the emphasis on a special point in the parameter space of three dimensional new massive gravity, using the so-called Fefferman-Graham coordinates with relevant counter terms. Through the linearized equations of motion with a standard prescription, we also obtain correlators among these stress tensors. We argue that the self-consistency of holographic renormalization determines counter terms up to unphysical ambiguities. Using these renormalized stress tensors in Fefferman-Graham coordinates, we obtain the central charges of dual CFT, and mass and angular momentum of some $AdS$ black hole solutions. These results are consistent with the previous ones obtained by other methods. In this study on the Fefferman-Graham expansion of new massive gravity, some aspects of higher curvature gravity are revealed.