New Massive Gravity and AdS_4 counterterms
Dileep P. Jatkar, Aninda Sinha
TL;DR
This theory is rewritten in terms of the gauge field that is used to recast 3D gravity as a Chern-Simons theory and the parameter values of the resulting counterterm action correspond to a c=0 theory in the context of the duality between AdS(3) gravity and two-dimensional conformal field theory.
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.