Some (3+1) dimensional vortex solutions of the CPN model

TL;DR

This paper introduces vortex-like solutions in the (3+1)-dimensional CPN model, analyzing their properties, energy behaviors, and charge densities, contributing to the understanding of topological solitons in higher dimensions.

Contribution

It presents new vortex solutions in the (3+1)D CPN model and examines their energetic and charge properties, which were not previously explored.

Findings

Some vortex configurations have divergent energy per unit length.

Certain vortex orientations minimize energy.

Noether charge densities are characterized for these vortices.

Abstract

We present a class of solutions of the CPN model in (3+1) dimensions. We suggest that they represent vortex-like configurations. We also discuss some of their properties. We show that some configurations of vortices have a divergent energy per unit length while for the others such an energy has a minimum for a very special orientation of vortices. We also discuss the Noether charge densities of these vortices.