One-loop beta-function for an infinite-parameter family of gauge theories

TL;DR

This paper demonstrates that an infinite-parameter family of gauge theories with a self-dual field strength component is one-loop renormalisable, with their beta-functions described by a single function's renormalisation group flow.

Contribution

It provides the first explicit calculation of the one-loop beta-function flow for an infinite family of gauge theories characterized by an arbitrary function of the self-dual field strength.

Findings

All divergences can be absorbed by field redefinitions and coupling renormalisations.

The family of theories is proven to be one-loop renormalisable.

The beta-functions are encapsulated in a single explicit flow equation.

Abstract

We continue to study an infinite-parametric family of gauge theories with an arbitrary function of the self-dual part of the field strength as the Lagrangian. The arising one-loop divergences are computed using the background field method. We show that they can all be absorbed by a local redefinition of the gauge field, as well as multiplicative renormalisations of the couplings. Thus, this family of theories is one-loop renormalisable. The infinite set of beta-functions for the couplings is compactly stored in a renormalisation group flow for a single function of the curvature. The flow is obtained explicitly.