Yang-Mills theory in the maximal Abelian gauge in presence of scalar matter fields

TL;DR

This paper proves that SU(2) Yang-Mills theories with scalar matter fields in the maximal Abelian gauge are multiplicatively renormalizable at all orders, accounting for complex ghost interactions introduced by the gauge's non-linearity.

Contribution

It introduces a BRST invariant action including new quartic interactions between scalar fields and ghosts, demonstrating all-order renormalizability.

Findings

The theory remains renormalizable with scalar matter fields.

Quartic interactions between scalar fields and ghosts are essential.

All-order multiplicative renormalizability is established.

Abstract

We address the issue of the all order multiplicative renormalizability of SU(2) Yang-Mills theories quantized in the maximal Abelian gauge in presence of scalar matter fields. The non-linear character of the maximal Abelian gauge requires the introduction of quartic interaction terms in the Faddeev-Popov ghosts, a well known feature of this gauge. We show that, when scalar matter fields are introduced, a second quartic interaction term between scalar fields and Faddeev-Popov ghosts naturally arises. A BRST invariant action accounting for those quartic interaction terms is identified and proven to be multiplicative renormalizable to all orders by means of the algebraic renormalization procedure.