Semilocal strings and monopoles

Abstract

A variation on the abelian Higgs model, with SU(2)global x U(1)local symmetry broken to U(1)global, was recently shown by Vachaspati and Achucarro to admit stable, finite-energy cosmic string solutions, even though the manifold of minima of the potential energy does not have non-contractible loops. This new and unexpected feature motivates a full investigation of the properties of the model. Here we exploit the existence of first-order Bogomol'nyi equations to classify all static finite-energy vortex solutions in the Bogomol'nyi limit. We find a 4n-dimensional moduli space for the nth topological (n-vortex) sector. Single-vortex configurations depend on a position coordinate and on an additional complex parameter and may be regarded as hybrids of Nielsen-Olesen vortices and CP1 lumps. The model is also shown to obey Bogomol'nyi equations in curved space, and these allow a simple calculation of the gravitational field of the above configurations. Finally, monopole-like solutions interpolating between a Dirac monopole and a global monopole are found. These must be surrounded by an event horizon as isolated solutions, but may also arise as unstable end points of semi-local strings.