The Ward identity of Symmetry Breaking from Holographic Renormalization

TL;DR

This paper demonstrates how holographic renormalization can be used to derive Ward identities related to symmetry breaking, including both spontaneous and explicit cases, with applications to non-relativistic theories.

Contribution

It provides a systematic derivation of Ward identities for symmetry breaking using holographic renormalization, extending the Goldstone theorem to non-relativistic contexts.

Findings

Derived Ward identities for symmetry breaking in holography

Extended Goldstone theorem to non-relativistic theories

Illustrated derivation with a concrete holographic example

Abstract

Notes on holographic renormalization as a tool for UV analysis and derivation of the two-point Ward identity encoding symmetry breaking. Goldstone theorem is reviewed, discussing in particular the modifications required by its extension to non-relativistic field theories. The Ward identity encoding both spontaneous and explicit breaking are derived by general principles. Holographic renormalization is presented in a quite operational fashion. The derivation of the Ward identity in holography is illustrated by an example.