A Note On Holographic Ward Identities

TL;DR

This paper demonstrates how to derive Ward identities in a dual quantum field theory from bulk gauge symmetries in string theory using the AdS/CFT correspondence, via Hamilton-Jacobi constraints.

Contribution

It introduces a method to obtain Ward identities from bulk supergravity constraints in the AdS/CFT framework, illustrated with multiple examples.

Findings

Ward identities derived from bulk gauge symmetries

Hamilton-Jacobi form generates dual QFT constraints

Method applicable to various supergravity models

Abstract

In this note we show how Ward identities may be derived for a quantum field theory dual of a string theory using the AdS/CFT correspondence. In particular associated with any gauge symmetry of the bulk supergravity theory there is a corresponding constraint equation. Writing this constraint in Hamilton-Jacobi form gives a generating functional for Ward identities in the dual QFT. We illustrate the method by considering various examples.