CLASSICAL AND CHERN-SIMONS VORTICES ON CURVED SPACE

Abstract

The classical dynamics of some vortex models coupled to gravity in the critical coupling is considered. We derive the set of Bogomol’nyi-type equations of motion for the Abelian Higgs model and for the Chern-Simons vortex model, coupled to gravity. In both cases we are able to reduce the dynamics to a single nonlinear equation which generalizes, on a curved space, the corresponding vortex equation on the plane. We finally compute in both cases the asymptotic behavior for a multivortex configuration from the N particle metric without and with spin, respectively.