Surface Terms as Counterterms in the AdS/CFT Correspondence

TL;DR

This paper explores the use of boundary counterterms in the AdS/CFT correspondence to regularize gravitational actions, extending the method to higher dimensions and applying it to various black hole solutions, with implications for dual field theories.

Contribution

It explicitly identifies higher order counterterms for dimensions up to seven, enabling background-independent calculations of gravitational actions in asymptotically AdS spacetimes.

Findings

Counterterms eliminate background subtraction in action calculations.

Application to topological black holes and Taub-NUT/Bolt-AdS spacetimes.

Limit to flat spacetime recovers known results and clarifies ambiguities.

Abstract

We examine the recently proposed technique 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<=7. 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 ambiguous or unknown: topological black holes, Taub-NUT-AdS and Taub-Bolt-AdS. 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. In some examples, the case of vanishing cosmological constant may be recovered in a limit, which allows us to check results and resolve ambiguities in certain asymptotically flat spacetime computations in the literature.