The spectrum of Bogomolʹnyi solitons in gauged linear sigma models Original Research Article

Gauged linear sigma models with Cm-valued scalar fields and gauge group U(1)d, d ⩽ m, have soliton solutions of Bogomolʹnyi 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 Bogomolʹnyi 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. CPm-1 textures and gauged CPm-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 Chem-Simons term instead of a Maxwell term a different scalar potential is required for the theory to be of Bogomolʹnyi type. The general form of that potential is given and a particular example is discussed.