Bogomol'nyi Solitons and Hermitian Symmetric Spaces

We construct relativistic nonlinear sigma models on the target space of coadjoint orbits coupled with the Chern-Simons field and study self-dual solitons. When the target space is given by the Hermitian symmetric spaces, we find that these solitons saturate the Bogomol'nyi bound of the energy functional which is bounded from below by a topological charge. The Bogomol'nyi potential on the arbitrary Hermitian symmetric spaces is obtained in the case when the maximal torus subgroup is gauged, and the self-dual equations in the $CP(N-1)$ case is explored. We also discuss the nonrelativistic limit and find that it yields the previous Chern-Simons Heisenberg ferromagnet model of easy-axis type