Sigma models coupled with Abelian gauge fields

Two distinct Skyrme terms for the CP1 model are defined, only one of which preserves the equivalence with the corresponding O(3) model. A gauging pres cription in which the composite connection of the CP1 model is replaced by the U(1) gauge connection is defined. A U(1) gauged CP1 model and two disti nct U(1) gauged CP1 models with Skyrme terms are defined. The existence of topologically stable vortices in each of the three U(1) gauged models is pr oved analytically. (C) 1998 American Institute of Physics. [S0022-2488(98)0 2211-7].