Bogomol'nyi Solitons and Hermitian Symmetric Spaces

Details Bogomol'nyi Solitons and Hermitian Symmetric Spaces Bogomol'nyi Solitons and Hermitian Symmetric Spaces

1997-07-17

arxiv.org/abs/hep-th/9707150v3

Rept.Math.Phys.43:271-281,1999

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, 2 ps figures, Latex, A revised version to be published in Reports on Mathematical Physics

Scientific paper

10.1016/S0034-4877(99)80035-4

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 study self-dual solitons. When the target space is given by 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 non-compact $SU(1,1)$ case and present a detailed analysis for the rotationally symmetric solutions.

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