A gauge invariant exact renormalization group I

TL;DR

This paper develops a gauge invariant renormalization group flow equation for pure SU(N) gauge theory, enabling calculations without gauge fixing and expressing the effective action through Wilson loops.

Contribution

It introduces a gauge invariant flow equation for SU(N) gauge theories that avoids gauge fixing and uses Wilson loops, with a simplified form at infinite N.

Findings

Flow equation is gauge invariant and does not require gauge fixing.

Effective action expressed as a gas of Wilson loops.

Regularization of flow equations is necessary, discussed in part II.

Abstract

A manifestly gauge invariant continuous renormalization group flow equation is constructed for pure SU(N) gauge theory. The formulation makes sense without gauge fixing and manifestly gauge invariant calculations may thus be carried out. The flow equation is naturally expressed in terms of fluctuating Wilson loops, with the effective action appearing as an integral over a `gas' of Wilson loops. At infinite N, the effective action collapses to a path integral over the trajectory of a single particle describing one Wilson loop. We show that further regularization of these flow equations is needed. (This is introduced in part II.)