Bogomol'nyi solitons and Hermitian symmetric spaces

We apply the coadjoint orbit method to construct relativistic nonlinear sig ma models (NLSM) on the target space of coadjoint orbits coupled with the C hern-Simons (CS) gauge field and we study self-dual solitons. When the targ et space is given by a Hermitian symmetric space (HSS), we find that the sy stem admits self-dual solitons whose energy is Bogomol'nyi bounded from bel ow by a topological charge. The Bogomol'nyi potential on the Hermitian symm etric space is obtained in the case when the maximal torus subgroup is gaug ed, and the self-dual equation in the CP(N - 1) case is explored. We also d iscuss the self-dual solitons in the case of noncompact SU(1, 1) and presen t a detailed analysis for the rotationally symmetric solutions.