The self-dual Chern-Simons $CP(N)$ models

TL;DR

This paper investigates self-dual Chern-Simons $CP(N)$ models with a global $U(1)$ symmetry, revealing their vacuum and soliton structures and generalizing Bogomolnyi bounds.

Contribution

It introduces self-dual Chern-Simons $CP(N)$ models with a generalized Bogomolnyi bound and explores their rich vacuum and soliton configurations.

Findings

Identified self-dual models within the Chern-Simons $CP(N)$ framework.

Established a generalized Bogomolnyi bound for these models.

Showed the models' relation to known gauged self-dual models.

Abstract

We study the Chern-Simons $CP(N)$ models with a global $U(1)$ symmetry and found the self-dual models among them. The Bogomolnyi-type bound in these self-dual models is a nontrivial generalization of that in the pure $CP(N)$ models. Our models have quite a rich vacuum and soliton structure and approach the many known gauged self-dual models in some limit.