Holographic Weyl Anomaly and Kounterterms in AdS gravity

TL;DR

This paper demonstrates how Kounterterms in Einstein-AdS gravity facilitate the extraction of holographic conformal anomalies, especially Weyl anomalies, in odd-dimensional spacetimes with a finite action.

Contribution

It shows how to derive holographic conformal anomalies from the variation of Einstein-AdS gravity with Kounterterms in arbitrary odd dimensions.

Findings

Partial renormalization of AdS gravity using Kounterterms

Explicit extraction of Weyl anomalies in odd dimensions

Closed-form variation of the action in arbitrary dimensions

Abstract

The addition of Kounterterms to Einstein gravity leads to a finite action for asymptotically anti-de Sitter (AdS) spaces with a conformally flat boundary. In that sense, it provides a partial renormalization for AdS gravity when compared to standard holographic techniques, where the mismatch is given in terms of nontrivial conformal properties of the boundary. On the other hand, this method has the clear advantage that the variation of the action has a closed form in an arbitrary dimension. In this work, it is shown how to extract holographic information on conformal anomalies from the variation in $(2n+1)$-dimensional Einstein-AdS plus Kounterterms. Remarkably enough, a considerable part of the Weyl anomaly can be worked out for any odd dimension.