# Gauge invariance of the background average effective action

## TL;DR

This paper investigates how the background average effective action in gauge theories maintains gauge invariance and how gauge fixing dependence persists on-shell, using the background field method within the functional renormalization group framework.

## Contribution

It demonstrates that background field symmetry can be preserved for many regulator functions, clarifying gauge dependence issues in the background average effective action.

## Key findings

- Symmetry can be maintained for a wide class of regulators.
- Gauge dependence of the effective action remains on-shell.
- Application to Yang-Mills theory illustrates the results.

## Abstract

Using the background field method for the functional renormalization group approach in the case of a generic gauge theory, we study the background field symmetry and gauge dependence of the background average effective action, when the regulator action depends on external fields. The final result is that the symmetry of the average effective action can be maintained for a wide class of regulator functions, but in all cases the dependence of the gauge fixing remains on-shell. The Yang-Mills theory is considered as the main particular example.