The Spectrum of Bogomol'nyi Solitons in Gauged Linear Sigma Models

Abstract

Gauged linear sigma models with C^m-valued scalar fields and gauge group U(1)^d, d \leq m, have soliton solutions of Bogomol'nyi type if a suitably chosen potential for the scalar fields is also included in the Lagrangian. Here such models are studied on (2+1)-dimensional Minkowski space. If the dynamics of the gauge fields is governed by a Maxwell term the appropriate potential is a sum of generalised Higgs potentials known as Fayet-Iliopoulos D-terms. Many interesting topological solitons of Bogomol'nyi type arise in models of this kind, including various types of vortices (e.g. Nielsen-Olesen, semilocal and superconducting vortices) as well as, in certain limits, textures (e.g. CP^(m-1) textures and gauged CP^(m-1) textures). This is explained and general results about the spectrum of topological defects both for broken and partially broken gauge symmetry are proven. When the dynamics of the gauge fields is governed by a Chern-Simons term instead of a Maxwell term a different scalar potential is required for the theory to be of Bogomol'nyi type. The general form of that potential is given and a particular example is discussed.