An exact RG formulation of quantum gauge theory

TL;DR

This paper develops a gauge-invariant Wilsonian effective action for SU(N) Yang-Mills theory using a novel flow equation, enabling calculations without gauge fixing or ghosts, and demonstrates the one-loop beta function computation.

Contribution

It introduces a new exact RG formulation that maintains gauge invariance and avoids gauge fixing, using a spontaneously broken SU(N|N) supergauge regularisation.

Findings

Successfully computed the one-loop beta function without gauge fixing

Established a manifestly gauge-invariant flow equation for Yang-Mills theory

Proposed a novel regularisation method via supergauge theory

Abstract

A gauge invariant Wilsonian effective action is constructed for pure SU(N) Yang-Mills theory by formulating the corresponding flow equation. Manifestly gauge invariant calculations can be performed i.e. without gauge fixing or ghosts. Regularisation is implemented in a novel way which realises a spontaneously broken SU(N|N) supergauge theory. As an example we sketch the computation of the one-loop beta function, performed for the first time without any gauge fixing.