Simple recipe for holographic Weyl anomaly

TL;DR

This paper introduces a simple method to compute the holographic Weyl anomaly for higher-derivative gravity in AdS spaces, enabling straightforward extraction of anomaly coefficients in dual CFTs.

Contribution

It presents a minimalistic recipe using a basis of curvature invariants to efficiently determine Weyl anomaly coefficients in 5 and 7 dimensions.

Findings

Successfully tabulated contributions from various curvature invariants.

Validated the method with examples matching previous results.

Simplified the computation process for holographic Weyl anomalies.

Abstract

We propose a recipe - arguably the simplest - to compute the holographic type-B Weyl anomaly for general higher-derivative gravity in asymptotically AdS spacetimes. In 5 and 7 dimensions we identify a suitable basis of curvature invariants that allows to read off easily, without any further computation, the Weyl anomaly coefficients of the dual CFT. We tabulate the contributions from quadratic, cubic and quartic purely algebraic curvature invariants and also from terms involving derivatives of the curvature. We provide few examples, where the anomaly coefficients have been obtained by other means, to illustrate the effectiveness of our prescription.