Properties of some (3+1) dimensional vortex solutions of the CP^N model

TL;DR

This paper constructs new (3+1) dimensional vortex solutions for the CP^N model, revealing evolving vortex-antivortex configurations with infinite energy, and explores their dynamic properties.

Contribution

It generalizes two-dimensional CP^N vortex techniques to (3+1) dimensions, introducing new solutions and analyzing their evolving, infinite-energy vortex dynamics.

Findings

Solutions describe evolving vortices with infinite energy

Configurations include vortex-antivortex pairs

Energy density varies over time

Abstract

We construct new classes of vortex-like solutions of the CP^N model in (3+1) dimensions and discuss some of their properties. These solutions are obtained by generalizing to (3+1) dimensions the techniques well established for the two dimensional CP^N models. We show that as the total energy of these solutions is infinite, they describe evolving vortices and anti-vortices with the energy density of some configurations varying in time. We also make some further observations about the dynamics of these vortices.