A gauge invariant regulator for the ERG

TL;DR

This paper proposes a gauge invariant regularisation method for pure Yang-Mills theories within the exact renormalization group framework, utilizing covariant higher derivatives and auxiliary fields, ensuring UV finiteness and a proper limit as the cutoff is removed.

Contribution

It introduces a novel gauge invariant regularisation scheme based on SU(N|N) super-gauge theory, advancing the handling of Yang-Mills theories in the ERG approach.

Findings

Perturbative proof of ultra-violet finiteness in four dimensions.

Demonstration of a sensible limit as the regularization cutoff is removed.

Implementation of auxiliary Pauli-Villars fields for gauge invariance.

Abstract

A gauge invariant regularisation for dealing with pure Yang-Mills theories within the exact renormalization group approach is proposed. It is based on the regularisation via covariant higher derivatives and includes auxiliary Pauli-Villars fields which amounts to a spontaneously broken SU(N|N) super-gauge theory. We demonstrate perturbatively that the extended theory is ultra-violet finite in four dimensions and argue that it has a sensible limit when the regularization cutoff is removed.