Self-dual Gauged $CP^N$ Models

TL;DR

This paper introduces a gauged $CP^N$ model with a nonabelian Chern-Simons term, deriving self-dual equations and analyzing soliton solutions with topological and global charges.

Contribution

It formulates self-dual equations for a gauged $CP^N$ model with a Chern-Simons term and explores soliton solutions with specific charge bounds.

Findings

Energy bounded by topological and $U(1)$ charges.

Derived self-dual equations for the model.

Discussed properties of soliton solutions.

Abstract

We consider a $CP^N$ model with the subgroup $SU(r)$ completely gauged, where $1 < r < N+1$. The gauge field dynamics is solely governed by a nonabelian Chern-Simons term and the global $SU(N+1)$ symmetry is broken explicitly by introducing a $SU(r)$ invariant scalar potential. We obtain self-dual equations of this gauged $CP^N$ model and find that the energy is bounded from below by a linear combination of the topological charge and a global $U(1)$ charge present in the theory. We also discuss on the self-dual soliton solutions of this model.