SELF-DUAL SOLITONS IN N=2 SUPERSYMMETRIC SEMILOCAL CHERN–SIMONS THEORY

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 shown 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.