Chern-Simons Vortices in Supergravity

TL;DR

This paper constructs supersymmetric vortex solutions in three-dimensional supergravity, revealing their geometric properties and supersymmetry preservation, and clarifies the connection between local supersymmetry and scalar potentials.

Contribution

It provides the first explicit construction of supersymmetric vortex solutions in 3D supergravity with a general Kahler scalar sector, linking local supersymmetry to scalar potential forms.

Findings

Existence of rotationally symmetric vortex solutions preserving half of the supersymmetry.

Asymptotically conical geometry of the vortex solutions.

Embedding of the abelian Chern-Simons Higgs model into 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 Kahler 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.