Formation of non-Abelian monopoles connected by strings

Abstract

We study the formation of monopoles and strings in a model where SU(3) is spontaneously broken to U(2)=[SU(2)xU(1)]/Z{sub 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 CP{sup 2}. To study the formation of these monopoles, we explicitly describe an algorithm to detect topologically nontrivial mappings on CP{sup 2}. The second symmetry breaking creates Z{sub 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.