Gauge invariance and background field formalism in the exact renormalisation group

TL;DR

This paper explores how gauge invariance is maintained within the exact renormalisation group framework for Yang-Mills theories using the background field formalism, ensuring gauge symmetry restoration as the cutoff is removed.

Contribution

It introduces a gauge invariant effective action construction within the Wilsonian flow approach using the background field method for pure Yang-Mills theories.

Findings

Gauge invariance is preserved in the effective action.

Symmetries are restored in the limit of removing the cutoff.

Separate evaluation of gauge transformations for gauge and background fields.

Abstract

We discuss gauge symmetry and Ward-Takahashi identities for Wilsonian flows in pure Yang-Mills theories. The background field formalism is used for the construction of a gauge invariant effective action. The symmetries of the effective action under gauge transformations for both the gauge field and the auxiliary background field are separately evaluated. We examine how the symmetry properties of the full theory are restored in the limit where the cut-off is removed.