New Massive Gravity and AdS_4 counterterms
Dileep P. Jatkar, Aninda Sinha

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. 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 Schwarzschild black hole entropy in a cut-off independent manner. The parameter values of the resulting counterterm action correspond to a theory in the context of AdS/CFT. We rewrite this theory in terms of the gauge field that is used to recast 3D gravity as a Chern-Simons theory.
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