Holographic Renormalisation and Anomalies

TL;DR

This paper analyzes the Weyl anomaly within the holographic renormalization group framework using Hamilton-Jacobi methods, focusing on the breakdown of descent equations and implications for c-functions.

Contribution

It provides a detailed study of Weyl anomalies in holography, exploring the role of finite terms and the interpretation of descent equations in non-perturbative RG flows.

Findings

Identification of conditions for anomaly form correction

Insights into the relation between bare and renormalized schemes

Proposal of a class of c-functions from descent equations

Abstract

The Weyl anomaly in the Holographic Renormalisation Group as implemented using Hamilton-Jacobi language is studied in detail. We investigate the breakdown of the descent equations in order to isolate the Weyl anomaly of the dual field theory close to the (UV) fixed point. We use the freedom of adding finite terms to the renormalised effective action in order to bring the anomalies in the expected form. We comment on different ways of describing the bare and renormalised schemes, and on possible interpretations of the descent equations as describing the renormalisation group flow non-perturbatively. We find that under suitable assumptions these relations may lead to a class of c-functions.