Gauge invariance, background fields and modified Ward identities

TL;DR

This paper discusses gauge invariance in Wilsonian flows of pure Yang-Mills theories, using background field formalism and modified Ward identities to analyze symmetry properties and their restoration as the cutoff is removed.

Contribution

It introduces a gauge invariant effective action in Yang-Mills theories using background fields and modified Ward identities, clarifying symmetry restoration at the cutoff limit.

Findings

Gauge invariance is maintained in the effective action.

Separate gauge transformations for gauge and background fields are analyzed.

Symmetry properties are restored when the cutoff is removed.

Abstract

In this talk the gauge symmetry for Wilsonian flows in pure Yang-Mills theories is discussed. 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. Modified Ward-Takahashi and background field identities are used in my study. Finally it is shown how the symmetry properties of the full theory are restored in the limit where the cut-off is removed.