Chern-Simons vortices in supergravity

Abstract

We study supersymmetric vortex solutions in three-dimensional Abelian gauged supergravity. First, we construct the general $U(1)$-gauged $D=3,$ $N=2$ supergravity whose scalar sector is an arbitrary K\"ahler manifold with $U(1)$ isometry. This construction clarifies the connection between local supersymmetry and the specific forms of some scalar potentials previously found in the literature---in particular, it provides the locally supersymmetric embedding of the Abelian Chern-Simons Higgs model. We show that the Killing spinor equations admit rotationally symmetric vortex solutions with asymptotically conical geometry which preserve half of the supersymmetry.