Non-Fefferman-Graham asymptotics and holographic renormalization in New Massive Gravity

TL;DR

This paper investigates the asymptotic structure of New Massive Gravity, revealing that traditional methods are insufficient and proposing new boundary conditions and counterterms for holographic renormalization.

Contribution

It introduces new asymptotic expansions and boundary conditions for NMG, capturing massive graviton modes and extending holographic renormalization techniques.

Findings

Traditional Fefferman-Graham expansion fails for NMG.

New boundary conditions are identified for specific mass ranges.

Holographically renormalized stress tensor is computed with new counterterms.

Abstract

The asymptotic behavior of new massive gravity (NMG) is analyzed for all values of the mass parameter satisfying the Breitenlohner-Freedman bound. The traditional Fefferman-Graham expansion fails to capture the dynamics of NMG, and new terms in the asymptotic expansion are needed to include the massive graviton modes. New boundary conditions are discovered for a range of values $-1<2m^2l^2<1$ at which non-Einstein modes decay more slowly than the Brown-Henneaux boundary conditions. The holographically renormalized stress tensor is computed for these modes, and the relevant counterterms are identified up to unphysical ambiguities.