On the Functional Renormalization Group approach for Yang-Mills fields

TL;DR

This paper investigates the gauge dependence in the functional renormalization group approach for Yang-Mills fields and proposes a new formulation using composite operators to achieve on-shell gauge invariance.

Contribution

It introduces a novel FRG formulation with composite operators that ensures on-shell gauge invariance and universality of the S-matrix in Yang-Mills theories.

Findings

Standard FRG for Yang-Mills remains gauge-dependent on-shell.

New composite operator-based FRG formulation achieves gauge invariance on-shell.

Proposed method enhances the universality of the S-matrix.

Abstract

We explore the gauge dependence of the effective average action within the functional renormalization group (FRG) approach. It is shown that in the framework of standard definitions of FRG for the Yang-Mills theory, the effective average action remains gauge-dependent on-shell, independent on the use of truncation scheme. Furthermore, we propose a new formulation of the FRG, based on the use of composite operators. In this case one can provide on-shell gauge-invariance for the effective average action and universality of $S$-matrix.