Ward Identities for Invariant Group Integrals

TL;DR

This paper derives Ward identities for generating functions of invariant integrals of fundamental characters in simple compact Lie groups, providing new tools for analyzing group invariants.

Contribution

It introduces two types of Ward identities applicable to invariant integrals across arbitrary simple compact Lie groups, with specific applications to several rank 2 groups.

Findings

Derived Ward identities for SU(3), Spin(5), G_2, and SU(4)

Provided explicit formulas for invariant integrals

Enhanced understanding of group character invariants

Abstract

We derive two types of Ward identities for the generating functions for invariant integrals of monomials of the fundamental characters for arbitrary simple compact Lie groups. The results are applied to the groups SU(3), Spin(5) and G_2 of rank 2 as well as SU(4).