Surface terms as counterterms in the AdS-CFT correspondence - art. no. 104001

We examine the recently proposed technique of adding boundary counterterms to the gravitational action for spacetimes which are locally asymptotic to anti-de Sitter spacetimes. In particular, we explicitly identify higher ord er counrerterms, which allow us to consider spacetimes of dimensions d less than or equal to 7. As the counterterms eliminate the need of "background subtraction" in calculating the action, we apply this technique to study ex amples where the appropriate background was ambiguous or unknown: topologic al black holes, Taub-NUT-AdS and Taub-Bolt-AdS. We also identify certain ca ses where the covariant counterterms fail to render the action finite. and we comment on the dual field theory interpretation of this result. In some examples, the case of a vanishing cosmological constant may be recovered in a limit, which allows us to check results and resolve ambiguities in certa in asymptotically flat spacetime computations in the literature. [S0556-282 1(99)07318-X].