Bogomol'nyi Solitons and Hermitian Symmetric Spaces

TL;DR

This paper constructs and analyzes self-dual solitons in relativistic nonlinear sigma models on Hermitian symmetric spaces, revealing energy bounds and explicit solutions, and extends the study to non-compact cases with symmetric solutions.

Contribution

It introduces a novel application of the coadjoint orbit method to construct self-dual solitons on Hermitian symmetric spaces with explicit energy bounds and solutions.

Findings

Self-dual solitons exist with energies bounded by topological charges.

Explicit Bogomol'nyi potentials are derived for gauged Hermitian symmetric spaces.

Rotationally symmetric solutions are analyzed in both compact and non-compact cases.

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 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.