A Manifestly Gauge Invariant and Universal Calculus for SU(N) Yang-Mills

TL;DR

This paper develops a gauge-invariant calculus for SU(N) Yang-Mills within the Exact Renormalization Group framework, demonstrating that the beta function is independent of non-universal details through a diagrammatic proof.

Contribution

It introduces a universal, gauge-invariant calculus for SU(N) Yang-Mills that ensures the beta function's independence from specific cutoff details.

Findings

Beta function has no explicit dependence on seed action

Diagrammatic cancellation of non-universal contributions

Framework applicable to all orders in perturbation theory

Abstract

Within the framework of the Exact Renormalization Group, a manifestly gauge invariant calculus is constructed for SU(N) Yang-Mills. The methodology is comprehensively illustrated with a proof, to all orders in perturbation theory, that the beta function has no explicit dependence on either the seed action or details of the covariantization of the cutoff. The cancellation of these non-universal contributions is done in an entirely diagrammatic fashion.