Gauge dependence of effective action and renormalization group functions in effective gauge theories

TL;DR

This paper generalizes the gauge dependence analysis of the effective action and renormalization group functions to a broader class of gauge theories, showing how physical couplings can be redefined to eliminate gauge parameter dependence.

Contribution

It extends Caswell-Wilczek's analysis to non-renormalizable gauge theories, demonstrating gauge parameter independence of physical beta functions through redefinition of couplings.

Findings

Effective action can be made gauge parameter independent.

Physical beta functions are gauge independent after redefinition.

The approach applies to both renormalizable and non-renormalizable theories.

Abstract

The Caswell-Wilczek analysis on the gauge dependence of the effective action and the renormalization group functions in Yang-Mills theories is generalized to generic, possibly power counting non renormalizable gauge theories. It is shown that the physical coupling constants of the classical theory can be redefined by gauge parameter dependent contributions of higher orders in $\hbar$ in such a way that the effective action depends trivially on the gauge parameters, while suitably defined physical beta functions do not depend on those parameters.