New Massive Gravity and AdS_4 counterterms

TL;DR

This paper demonstrates that a DBI extension of new massive gravity naturally arises as an AdS_4 counterterm, leading to a cut-off independent Euclidean action and black hole entropy, with implications for AdS/CFT correspondence.

Contribution

It introduces a new counterterm in AdS_4 derived from massive gravity, linking it to a c=0 theory and Chern-Simons formulation, advancing holographic renormalization techniques.

Findings

Counterterm derived from massive gravity matches DBI extension.

On-shell Euclidean action is cut-off independent at zero temperature.

Black hole entropy follows the area law independently of cut-off.

Abstract

We show that the recently proposed DBI extension of new massive gravity emerges naturally as a counterterm in AdS$_4$. The resulting on-shell Euclidean action is independent of the cut-off at zero temperature. We also find that the same choice of counterterm gives the usual area law for the AdS$_4$ Schwarzschild black hole entropy in a cut-off independent manner. The parameter values of the resulting counterterm action correspond to a $c=0$ theory in the context of AdS$_3$/CFT$_2$. We rewrite this theory in terms of the gauge field that is used to recast 3D gravity as a Chern-Simons theory.