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

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.