Gauge invariant regularisation via SU(N|N)

TL;DR

This paper introduces a gauge invariant regularisation method for SU(N) Yang-Mills theory using covariant higher derivatives and supergauge invariance, ensuring finiteness and unitarity in the limit of removing the regulator.

Contribution

It develops a novel gauge invariant regularisation scheme for Yang-Mills theory employing SU(N|N) supergauge invariance and covariant higher derivatives, valid to all perturbation orders.

Findings

Regularisation preserves gauge invariance and unitarity.

All divergences are cured except for one-loop graphs, which are finite due to supergroup properties.

The scheme is proven to work to all orders in perturbation theory.

Abstract

We construct a gauge invariant regularisation scheme for pure SU(N) Yang-Mills theory in fixed dimension four or less (for N = infinity in all dimensions), with a physical cutoff scale Lambda, by using covariant higher derivatives and spontaneously broken SU(N|N) supergauge invariance. Providing their powers are within certain ranges, the covariant higher derivatives cure the superficial divergence of all but a set of one-loop graphs. The finiteness of these latter graphs is ensured by properties of the supergroup and gauge invariance. In the limit Lambda tends to infinity, all the regulator fields decouple and unitarity is recovered in the renormalized pure SU(N) Yang-Mills theory. By demonstrating these properties, we prove that the regularisation works to all orders in perturbation theory.