Surface Terms as Counterterms in the AdS/CFT Correspondence
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Abstract
We examine the recent proposal of adding boundary counterterms to the gravitational action for spacetimes which are locally asymptotic to anti-de Sitter. In particular, we explicitly identify higher order counterterms, which allow us to consider spacetimes of dimensions d<8. As the counterterms eliminate the need of ``background subtraction'' in calculating the action, we apply this technique to study examples where the appropriate background was unknown or ambiguous: topological black holes, Taub-NUT-AdS and Taub-Bolt-AdS. For the most part, we find that the results are consistent with those found in earlier studies, including the case of vanishing cosmological constant, which is recovered as a limit. We also identify certain cases where the covariant counterterms fail to render the action finite, and we comment on the dual field theory interpretation of this result.Keywords
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