Counterterms and dual holographic anomalies in CS gravity

TL;DR

This paper investigates the holographic Weyl anomaly in Chern-Simons gravity, showing it relates to the Euler term and deriving the associated energy-momentum tensor with Lovelock counterterms in odd dimensions.

Contribution

It provides a direct computation of the holographic energy-momentum tensor in Chern-Simons gravity and identifies the Lovelock-type counterterms needed for finiteness.

Findings

Holographic Weyl anomaly is proportional to the Euler term in 2n dimensions.

Counterterms are of Lovelock type, ensuring finiteness of the action.

Explicit computation of the energy-momentum tensor in arbitrary odd dimensions.

Abstract

The holographic Weyl anomaly associated to Chern-Simons gravity in 2n+1 dimensions is proportional to the Euler term in 2n dimensions, with no contributions from the Weyl tensor. We compute the holographic energy-momentum tensor associated to Chern-Simons gravity directly from the action, in an arbitrary odd-dimensional spacetime. We show, in particular, that the counterterms rendering the action finite contain only terms of the Lovelock type.