The Gauge Invariant ERG

TL;DR

This paper develops a gauge invariant formulation of the Exact Renormalization Group (ERG), enabling the first manifestly gauge invariant two-loop beta-function calculation, advancing non-perturbative gauge theory analysis.

Contribution

It introduces a novel gauge invariant ERG framework and demonstrates its application to compute the two-loop beta-function in a gauge invariant manner.

Findings

Successful construction of a gauge invariant ERG formalism

First gauge invariant two-loop beta-function calculation

Enhanced tools for non-perturbative gauge theory studies

Abstract

We sketch the construction of a gauge invariant Exact Renormalization Group (ERG). Starting from Polchinski's equation, the emphasis is on how a series of ideas have combined to yield the gauge invariant formalism. A novel symmetry of the ERG allows the flow equation to be modified, in such a way that it is suitable for the computation of the (universal) two-loop beta-function. This computation has now been performed, within the framework of the ERG and, as such, in a manifestly gauge invariant way for the very first time.