Holographic Renormalization of New Massive Gravity

TL;DR

The study performs holographic renormalization of three-dimensional New Massive Gravity at the critical point $m^2l^2=1/2$, where the dual CFT central charges vanish and logarithmic boundary behavior emerges. By employing Fefferman–Graham coordinates and a perturbative log boundary expansion, the authors identify a log source for an irrelevant operator and compute the regularized on-shell action. They derive the two-point functions of the energy-momentum tensor and its logarithmic partner, finding LCFT-type correlators with $c_L=c_R=0$ and anomaly $b=12/G$, in both holomorphic and anti-holomorphic sectors. These results support a parity-symmetric LCFT dual to NMG at the critical point and clarify the necessary boundary terms and counterterms for holographic renormalization.

Abstract

We study holographic renormalization for three dimensional new massive gravity (NMG). By studying the general fall off conditions for the metric allowed by the model at infinity, we show that at the critical point where the central charges of the dual CFT are zero it contains a leading logarithmic behavior. In the context of AdS/CFT correspondence it can be identified as a source for an irrelevant operator in the dual CFT. The presence of the logarithmic fall off may be interpreted as the fact that the dual CFT would be a LCFT.