Bogomol’nyi Solitons and Hermitian Symmetric Spaces

We apply the coadjoint orbit method to construct relativistic nonlinear sigma models (NLSM) on the target space of coadjoint orbits coupled with the ChernSimons (CS) gauge field and study self-dual solitons. When the target space is given by Hermitian symmetric space (HSS), we find that the system admits selfdual solitons whose energy is Bogomol’nyi bounded from below by a topological charge. The Bogomol’nyi potential on the Hermitian symmetric space is obtained in the case when the maximal torus subgroup is gauged, and the self-dual equation in the CP (N − 1) case is explored. We also discuss the self-dual solitons in the non-compact SU(1, 1) case and present a detailed analysis for the rotationally symmetric solutions.