Semilocal strings and monopoles

TL;DR

This work shows that stable, finite-energy semilocal strings can exist in a model with $SU(2)$ global and $U(1)$ local symmetry broken to a global $U(1)$, even though the vacuum manifold is topologically $S^3$. In the Bogomol'nyi limit, the authors derive the complete flat-space $n$-vortex solutions and reveal a rich one-vortex family parameterized by a complex modulus, connecting Nielsen–Olesen vortices and $CP^1$ lumps; they also determine the gravitational fields of these strings. Extending to curved space, they establish a Bogomol'nyi bound for the deficit angle and show the string spacetimes are asymptotically conical with deficit $\delta = 8\pi G n \eta^2$. Additionally, they construct monopole-like solutions in the Einstein–Maxwell–Higgs system that can be hidden behind horizons, describing both sigma-model and gauge-decoupled limits that yield diverse asymptotics, including possible cosmological relevance. Overall, the paper advances understanding of non-topological solitons in semilocal theories and their gravitational interactions, including novel monopole-like configurations with horizons.

Abstract

A variation on the abelian Higgs model, with global SU(2) x local U(1) symmetry broken to global U(1) 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. Here the most general solutions, both in the single and multi-vortex cases, are described in the Bogomol'nyi limit. The gravitational field of the vortices considered as cosmic strings is obtained and monopole-like solutions surrounded by an event horizon are found.