Self-Dual Chern-Simons Solitons and Generalized Heisenberg Ferromagnet Models

TL;DR

This paper explores self-dual solitons in a (2+1)-dimensional gauged Heisenberg ferromagnet model coupled with Chern-Simons fields, revealing new vortex solutions valued in Hermitian symmetric spaces and extending instanton concepts.

Contribution

It demonstrates the existence of self-dual Chern-Simons solitons in generalized spin models valued in Hermitian symmetric spaces, including explicit solutions for CP(N).

Findings

Self-dual solitons exist in the model when the spin variable is in G/H.

Gauging the maximal torus yields vortex-type nonlinear equations.

Explicit CP(N) solutions are provided.

Abstract

We consider the (2+1)-dimensional gauged Heisenberg ferromagnet model coupled with the Chern-Simons gauge fields. Self-dual Chern-Simons solitons, the static zero energy solution saturating Bogomol'nyi bounds, are shown to exist when the generalized spin variable is valued in the Hermitian symmetric spaces G/H. By gauging the maximal torus subgroup of H, we obtain self-dual solitons which satisfy vortex-type nonlinear equations thereby extending the two dimensional instantons in a nontrivial way. An explicit example for the CP(N) case is given.