Formation of Non-Abelian Monopoles Connected by Strings

TL;DR

This paper investigates the formation and interactions of non-Abelian monopoles and strings in a specific symmetry-breaking model, providing algorithms and analyzing stability and distribution of defects relevant to grand unified theories.

Contribution

It introduces an explicit algorithm to detect topologically non-trivial mappings on  P^2 and analyzes monopole-string interactions in a two-stage symmetry-breaking model.

Findings

Monopoles with SU(2) and U(1) charges are formed during the first symmetry breaking.

 P^2 topology is used to detect monopoles.

The study determines the distribution and survival fraction of monopoles after string formation.

Abstract

We study the formation of monopoles and strings in a model where SU(3) is spontaneously broken to U(2)=[SU(2)\times U(1)]/\ZZ_2, and then to U(1). The first symmetry breaking generates monopoles with both SU(2) and U(1) charges since the vacuum manifold is \CC P^2. To study the formation of these monopoles, we explicitly describe an algorithm to detect topologically non-trivial mappings on \CC P^2. The second symmetry breaking creates \ZZ_2 strings linking either monopole-monopole pairs or monopole-antimonopole pairs. When the strings pull the monopoles together they may create stable monopoles of charge 2 or else annihilate. We determine the length distribution of strings and the fraction of monopoles that will survive after the second symmetry breaking. Possible implications for topological defects produced from the spontaneous breaking of even larger symmetry groups, as in Grand Unified models, are discussed.