Bogomol'nyi solitons and Hermitian symmetric spaces |
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Affiliation: | 1. Department of Physics, Sung Kyun Kwan University, Suwon 440-746, Republic of Korea;2. Center for Theoretical Physics, M.I.T., Cambridge, MA 02139-4307, USA |
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Abstract: | We apply the coadjoint orbit method to construct relativistic nonlinear sigma models (NLSM) on the target space of coadjoint orbits coupled with the Chern-Simons (CS) gauge field and we study self-dual solitons. When the target space is given by a Hermitian symmetric space (HSS), we find that the system admits self-dual 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 case of noncompact SU(1, 1) and present a detailed analysis for the rotationally symmetric solutions. |
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