Holography and the Weyl anomaly

TL;DR

The paper derives holographic Weyl anomalies for d-dimensional CFTs with (d+1)-dimensional gravity duals, using holographic renormalization and Fefferman-Graham expansion. It shows that the anomaly is determined by a single coefficient a_(d) and provides explicit d=2,4,6 results, including a 2D central charge, a 4D Euler/Weyl invariant combination, and a 6D higher-derivative curvature combination. The results reproduce known CFT and string/M-theory expectations: Brown-Henneaux central charge in AdS3, non-renormalization of the N=4 SYM anomaly, and N^3 scaling for M5-brane tensionless string theory. This supports the consistency of the holographic approach and offers concrete curvature-based expressions for the Weyl anomaly in diverse dimensions.

Abstract

We review our calculation of the Weyl anomaly for d-dimensional conformal field theories that have a description in terms of a (d + 1)-dimensional gravity theory.