Semilocal Topological Defects

Abstract

Semilocal defects are those formed in field theories with spontaneously broken symmetries, where the vacuum manifold $M$ is fibred by the action of the gauge group in a non-trivial way. Studied in this paper is the simplest such class of theories, in which $M\simeq S^{2N-1}$, fibred by the action of a local $U(1)$ symmetry. Despite $M$ having trivial homotopy groups up to $\pi_{2N-2}$, this theory exhibits a fascinating variety of defects: vortices, or semilocal strings; monopoles (on which the strings terminate); and (when $N=2$) textures, which may be stabilised by their associated magnetic field to produce a skyrmion.