A proposal for a manifestly gauge invariant and universal calculus in Yang-Mills theory

TL;DR

This paper introduces a gauge-invariant, universal calculus method for Yang-Mills theory that avoids gauge fixing and regularisation details, demonstrated through a one-loop beta function calculation.

Contribution

It presents a novel gauge-invariant calculation technique within the exact renormalization group framework, avoiding gauge fixing and regularisation scheme dependence.

Findings

Successfully computed the one-loop beta function without gauge fixing.

Achieved a manifestly universal result at finite N.

Demonstrated the diagrammatic initial stages of the method.

Abstract

We uncover a method of calculation that proceeds at every step without fixing the gauge or specifying details of the regularisation scheme. Results are obtained by iterated use of integration by parts and gauge invariance identities. The initial stages can even be computed diagrammatically. The method is formulated within the framework of an exact renormalization group for SU(N) Yang-Mills gauge theory, incorporating an effective cutoff through a manifest spontaneously broken SU(N|N) gauge invariance. We demonstrate the technique with a compact calculation of the one-loop beta function, achieving a manifestly universal result, and without gauge fixing, for the first time at finite N.