Explicit Multimonopole Solutions in SU(N) Gauge Theory

TL;DR

This paper constructs explicit multimonopole solutions in SU(N) gauge theory, detailing their properties and the structure of non-Abelian clouds in various symmetry-breaking scenarios.

Contribution

It provides explicit formulas for multimonopole configurations in SU(N) gauge theories, including the structure of non-Abelian clouds and their physical properties.

Findings

Explicit multimonopole solutions for all monopole positions and phases.

Description of monopole configurations with different symmetry breakings.

Analysis of non-Abelian cloud properties in monopole solutions.

Abstract

We construct multimonopole solutions containing N-1 distinct fundamental monopoles in SU(N) gauge theory. When the gauge symmetry is spontaneously broken to U(1)^{N-1}, the monopoles are all massive, and we show that the fields can be written in terms of elementary function for all values of the monopole positions and phases. In the limit of unbroken U(1) X SU(N-2) X U(1) symmetry, the configuration can be viewed as containing a pair of massive monopoles, each carrying both U(1) and SU(N-2) magnetic charges, together with N-3 massless monopoles that condense into a cloud of non-Abelian fields. We obtain explicit expressions for the fields in the latter case and use these to analyze the properties of the non-Abelian cloud.