New Massive Gravity and AdS_4 counterterms

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.

10 pages, v2: references added, minor changes, v3: minor changes, to appear in Physical Review Letters

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