A Manifestly Gauge Invariant, Continuum Calculation of the SU(N) Yang-Mills two-loop beta function

TL;DR

This paper presents a continuum, gauge-invariant calculation of the two-loop beta function in SU(N) Yang-Mills theory using the Exact Renormalisation Group, avoiding gauge fixing and specific regularisation schemes.

Contribution

It introduces a novel gauge-invariant formalism for computing the two-loop beta function in Yang-Mills theory without fixing the gauge or specifying regularisation details.

Findings

Successfully computed the two-loop beta function in a gauge-invariant manner

Demonstrated the formalism's independence from regularisation scheme details

Provided a new approach for continuum gauge theory calculations

Abstract

The manifestly gauge invariant Exact Renormalisation Group provides a framework for performing continuum computations in SU(N) Yang-Mills theory, without fixing the gauge. We use this formalism to compute the two-loop beta function in a manifestly gauge invariant way, and without specifying the details of the regularisation scheme.