Ward-Takahashi identity for Yang-Mills theory in the Exact Renormalization Group

TL;DR

This paper derives the Ward-Takahashi identity for Yang-Mills theory within the exact renormalization group framework, showing how gauge symmetry is maintained despite a momentum cutoff through composite operators.

Contribution

It extends previous methods to non-abelian gauge theories, providing a functional derivation of the Ward-Takahashi identity that accounts for cutoff-induced deformations of gauge symmetry.

Findings

Non-abelian gauge symmetry is realized nontrivially with a cutoff.

Composite operators encode the deformation of gauge transformations.

The method extends previous QED approaches to Yang-Mills theory.

Abstract

We give a functional derivation of the Ward-Takahashi identity for Yang-Mills theory in the framework of the exact renormalization group. The identity realizes non-abelian gauge symmetry nontrivially despite the presence of a momentum cutoff. The cutoff deforms the gauge transformation by introducing composite operators. In our functional method, which is an extension of the method used in our previous work on QED, these composite operators are expressed in terms of the Wilson action that depends on both a UV cutoff and an IR cutoff.