Self-dual solitons in N=2 supersymmetric semilocal Chern-Simons theory

TL;DR

This paper embeds semilocal Chern-Simons-Higgs theory into an N=2 supersymmetric framework, deriving BPS equations and demonstrating the existence and stability of supersymmetric cosmic string solutions.

Contribution

It constructs the supersymmetric extension, derives Bogomol'nyi equations, and analyzes the properties of BPS semilocal cosmic strings within this model.

Findings

Derivation of conserved supercharges and Bogomol'nyi equations.

Existence of string-like BPS solutions with magnetic flux concentration.

Supersymmetry ensures stability of solutions despite trivial vacuum topology.

Abstract

We embed the semilocal Chern-Simons-Higgs theory into an N=2 supersymmetric system. We construct the corresponding conserved supercharges and derive the Bogomol'nyi equations of the model from supersymmetry considerations. We show that these equations hold provided certain conditions on the coupling constants as well as on the Higgs potential of the system, which are a consequence of the huge symmetry of the theory, are satisfied. They admit string-like solutions which break one half of the supersymmetries --BPS Chern-Simons semilocal cosmic strings-- whose magnetic flux is concentrated at the center of the vortex. We study such solutions and show that their stability is provided by supersymmetry through the existence of a lower bound for the energy, even though the manifold of the Higgs vacuum does not contain non-contractible loops.