Gravitating self-dual cylindrical solutions in gauged sigma models

Cosmic strings and gravitating vortices are considered in gauged sigma models with either Maxwell or Chern-Simons terms. We obtain self-duality conditions for a general twodimensional target space which restrict the form of the scalar potential. In particular, we study the equations for the case of 0(3) models (two-sphere as target space), and find cosmic string solutions of several kinds as well as gravitating vortices. We classify the solutions by their flux and topological charge. We note an interesting connection between the Maxwell and Chern-Simons type models, which is responsible for simple relations between the self-dual solutions of both types.