Some properties of (3+1) dimensional vortex solutions in the extended CP^N Skyrme-Faddeev model

TL;DR

This paper investigates vortex solutions in the extended CP^N Skyrme-Faddeev model, revealing that holomorphic solutions are also solutions of the model, and discusses their dynamics and energy properties.

Contribution

It demonstrates that holomorphic solutions of the CP^N model are also solutions of the extended Skyrme-Faddeev model and analyzes their energy and dynamics.

Findings

Holomorphic solutions are also solutions of the extended model

Total energy of solutions is infinite, indicating time-dependent vortices

One energy term relates to the Noether charge

Abstract

We look at properties of vortex solutions of the extended CP^N Skyrme-Faddeev model. We show that only holomorphic solutions of the CP^N model are also solutions of the Skyrme-Faddeev model. As the total energy of these solutions is infinite these solutions should be interpreted as describing time dependent vortices. We describe their dynamics and, in partcular, point out that one of the terms in the energy density is related to the Noether charge of the model.