Monopoles, noncommutative gauge theories in the BPS limit and some simple gauge groups

TL;DR

This paper constructs and analyzes noncommutative monopole solutions in Yang-Mills-Higgs theories for specific gauge groups, revealing conditions under which these solutions exist and highlighting the physical significance of certain parameters.

Contribution

It provides explicit first-order noncommutative monopole solutions for SU(2), SU(3), and SO(5) gauge groups in the BPS limit, and identifies special parameter values affecting their existence.

Findings

Existence of noncommutative BPS monopoles depends on specific Seiberg-Witten map parameters.

Constructed smooth monopole and two-monopole solutions as formal power series in noncommutative parameter.

Certain parameters influence physical effects and are not mere gauge or field redefinition artifacts.

Abstract

For three conspicuous gauge groups, namely, SU(2), SU(3) and SO(5), and at first order in the noncommutative parameter matrix h\theta^{\mu\nu}, we construct smooth monopole --and, some two-monopole-- fields that solve the noncommutative Yang-Mills-Higgs equations in the BPS limit and that are formal power series in h\theta^{\mu\nu}. We show that there exist noncommutative BPS (multi-)monopole field configurations that are formal power series in h\theta^{\mu\nu} if, and only if, two a priori free parameters of the Seiberg-Witten map take very specific values. These parameters, that are not associated to field redefinitions nor to gauge transformations, have thus values that give rise to sharp physical effects.