A Generalised Manifestly Gauge Invariant Exact Renormalisation Group for SU(N) Yang-Mills

TL;DR

This paper extends a gauge-invariant renormalisation group approach for SU(N) Yang-Mills, enabling straightforward higher-loop calculations without gauge fixing or specific regularisation, and introduces diagrammatic methods for complex group structures.

Contribution

It generalises the manifestly gauge invariant exact renormalisation group to higher loops and develops new diagrammatic techniques for SU(N) Yang-Mills.

Findings

Successfully computed the two-loop beta function coefficient without gauge fixing.

Developed new diagrammatic methods for complex group theory calculations.

Enhanced the computational power of the gauge-invariant RG approach.

Abstract

We take the manifestly gauge invariant exact renormalisation group previously used to compute the one-loop beta function in SU(N) Yang-Mills without gauge fixing, and generalise it so that it can be renormalised straightforwardly at any loop order. The diagrammatic computational method is developed to cope with general group theory structures, and new methods are introduced to increase its power, so that much more can be done simply by manipulating diagrams. The new methods allow the standard two-loop beta function coefficient for SU(N) Yang-Mills to be computed, for the first time without fixing the gauge or specifying the details of the regularisation scheme.