Holographic Renormalization and Ward Identities with the Hamilton-Jacobi Method

TL;DR

This paper presents a systematic holographic renormalization procedure using the Hamilton-Jacobi method, enabling the calculation of divergences, anomalies, and Ward identities in a gravity-scalar-gauge field system.

Contribution

It introduces a novel Hamilton-Jacobi based approach for holographic renormalization, including divergence isolation and anomaly analysis, applicable to gravity theories with matter fields.

Findings

Derived explicit forms of divergences and anomalies.

Established Ward identities for diffeomorphisms and gauge invariance.

Confirmed the holographic chiral anomaly in the model.

Abstract

A systematic procedure for performing holographic renormalization, which makes use of the Hamilton-Jacobi method, is proposed and applied to a bulk theory of gravity interacting with a scalar field and a U(1) gauge field in the Stueckelberg formalism. We describe how the power divergences are obtained as solutions of a set of "descent equations" stemming from the radial Hamiltonian constraint of the theory. In addition, we isolate the logarithmic divergences, which are closely related to anomalies. The method allows to determine also the exact one-point functions of the dual field theory. Using the other Hamiltonian constraints of the bulk theory, we derive the Ward identities for diffeomorphisms and gauge invariance. In particular, we demonstrate the breaking of U(1)_R current conservation, recovering the holographic chiral anomaly recently discussed in hep-th/0112119 and hep-th/0202056.