Massive and massless monopoles with nonabelian magnetic charges

TL;DR

This paper investigates the properties of BPS monopoles with nonabelian magnetic charges using moduli space techniques, revealing how massless monopoles manifest as nonabelian clouds and relating these findings to duality conjectures.

Contribution

It provides a detailed analysis of nonabelian monopoles and their moduli spaces, introducing the concept of nonabelian clouds and connecting monopole properties to duality principles.

Findings

Massless monopoles appear as nonabelian clouds surrounding massive monopoles.

The moduli space metric encodes unbroken symmetries as isometries.

Results support the duality between massless monopoles and gauge bosons.

Abstract

We use the multimonopole moduli space as a tool for studying the properties of BPS monopoles carrying nonabelian magnetic charges. For configurations whose total magnetic charge is purely abelian, the moduli space for nonabelian breaking can be obtained as a smooth limit of that for a purely abelian breaking. As the asymptotic Higgs field is varied toward one of the special values for which the unbroken symmetry is enlarged to a nonabelian group, some of the fundamental monopoles of unit topological charge remain massive but acquire nonabelian magnetic charges. The BPS mass formula indicates that others should become massless in this limit. We find that these do not correspond to distinct solitons but instead manifest themselves as ``nonabelian clouds'' surrounding the massive monopoles. The moduli space coordinates describing the position and $U(1)$ phase of these massless monopoles are transformed into an equal number of nonabelian global gauge orientation and gauge-invariant structure parameters characterizing the nonabelian cloud. We illustrate this explicitly in a class of $Sp(2N)$ examples for which the full family of monopole solutions is known. We show in detail how the unbroken symmetries of the theory are manifested as isometries of the moduli space metric. We discuss the connection of these results to the Montonen-Olive duality conjecture, arguing in particular that the massless monopoles should be understood as the duals to the massless gauge bosons that appear as the mediators of the nonabelian forces in the perturbative sector.