Holographic Trace Anomaly and Cocycle of Weyl Group

TL;DR

This paper investigates the holographic trace anomaly and Weyl group cocycle within the AdS/CFT framework, revealing consistency between bulk and boundary cohomological structures of Weyl transformations.

Contribution

It establishes a detailed connection between the divergent part of the bulk effective action and the Weyl group cocycle, confirming theoretical predictions.

Findings

The holographic trace anomaly matches the boundary Weyl cocycle.

Finite diffeomorphisms induce a non-trivial cocycle in the Weyl group.

Results support the holographic correspondence for conformal anomalies.

Abstract

The behavior of the divergent part of the bulk AdS/CFT effective action is considered with respect to the special finite diffeomorphism transformations acting on the boundary as a Weyl transformation of the boundary metric. The resulting 1-cocycle of the Weyl group is in full agreement with the 1-cocycle of the Weyl group obtained from the cohomological consideration of the effective action of the corresponding CFT.