Multicloud solutions with massless and massive monopoles

TL;DR

This paper investigates the structure of massless monopole clouds in SU(6) gauge theories, developing an algebraic method to relate solutions and clarify the conditions for cloud formation.

Contribution

It introduces a Nahm-based algebraic procedure to analyze BPS solutions with both massive and massless monopoles, revealing how massless monopoles form distinct clouds.

Findings

Six massless monopoles condense into four clouds of two types

The algebraic procedure relates new solutions to known examples

Conditions for finite size cloud formation are identified

Abstract

Certain spontaneously broken gauge theories contain massless magnetic monopoles. These are realized classically as clouds of non-Abelian fields surrounding one or more massive monopoles. In order to gain a better understanding of these clouds, we study BPS solutions with four massive and six massless monopoles in an SU(6) gauge theory. We develop an algebraic procedure, based on the Nahm construction, that relates these solutions to previously known examples. Explicit implementation of this procedure for a number of limiting cases reveals that the six massless monopoles condense into four distinct clouds, of two different types. By analyzing these limiting solutions, we clarify the correspondence between clouds and massless monopoles, and infer a set of rules that describe the conditions under which a finite size cloud can be formed. Finally, we identify the parameters entering the general solution and describe their physical significance.