A manifestly gauge invariant exact renormalization group

TL;DR

This paper develops a gauge invariant exact renormalization group framework for non-Abelian gauge theories, enabling non-perturbative analysis without gauge fixing and demonstrating the calculation of the one-loop beta function.

Contribution

It introduces a manifestly gauge invariant renormalization group equation and a non-perturbative continuum Wilsonian effective action for pure non-Abelian gauge theory.

Findings

Constructed a gauge invariant RG equation without gauge fixing.

Defined a non-perturbative gauge invariant Wilsonian effective action.

Calculated the one-loop beta function without gauge fixing.

Abstract

In these lectures we describe the construction of a gauge invariant renormalization group equation for pure non-Abelian gauge theory. In the process, a non-perturbative gauge invariant continuum Wilsonian effective action is precisely defined. The formulation makes sense without gauge fixing and thus manifest gauge invariance may be preserved at all stages. In the large N limit (of SU(N) gauge theory) the effective action simplifies: it may be expressed through a path integral for a single particle whose trajectory describes a Wilson loop. Regularization is achieved with the help of a set of Pauli-Villars fields whose formulation follows naturally in this picture. Finally, we show how the one loop beta function was computed, for the first time without any gauge fixing.