Solitons in gauged Sigma models: 2 dimensions

A prescription for the gauging of 2-dimensional Sigma models is studied. This prescription satisfies the criterion that the U(1) gauged Sigma model supports topologically stable solitons, like its ungauged counterpart. The gauging is carried out separately for both Maxwell and Chern-Simons dynamics of the U(1) field and it is shown that independently of this dynamics and of the inclusion of all possible Skyrme terms, our criterion is fulfilled. In the Maxwell case, the vortices are presented in detail and are seen to have some interesting properties of their own.