A Note on the Weyl Anomaly in the Holographic Renormalization Group

TL;DR

This paper presents a Hamilton-Jacobi based method for calculating the holographic Weyl anomaly across dimensions, reproducing known results and discussing the holographic renormalization group’s role in parameter space.

Contribution

It introduces a new prescription for holographic Weyl anomaly calculation using Hamilton-Jacobi equations applicable in any dimension, connecting to existing formalisms.

Findings

Reproduces known Weyl anomaly results with the new method

Provides a framework linking holographic RG to renormalized trajectories

Clarifies the relation to previous analyses by Henningson and Skenderis

Abstract

We give a prescription for calculating the holographic Weyl anomaly in arbitrary dimension within the framework based on the Hamilton-Jacobi equation proposed by de Boer, Verlinde and Verlinde. A few sample calculations are made and shown to reproduce the results that are obtained to this time with a different method. We further discuss continuum limits, and argue that the holographic renormalization group may describe the renormalized trajectory in the parameter space. We also clarify the relationship of the present formalism to the analysis carried out by Henningson and Skenderis.