Potentials and the vortex solutions in the $CP^N$ Skyrme-Faddeev model

TL;DR

This paper explores vortex solutions in the extended $CP^N$ Skyrme-Faddeev model, introducing various potentials and demonstrating a broad spectrum of solutions beyond previously known exact solutions.

Contribution

It introduces new potentials linked to holomorphic solutions and numerical solutions, expanding the known solution space of the model.

Findings

Vortex solutions with finite energy per unit length exist in the model.

Solutions include waves propagating at the speed of light along vortices.

The model admits a wider range of solutions with different coupling constants.

Abstract

The extended Skyrme-Faddeev model possesses vortex solutions in a (3+1) dimensional Minkowski space-time with target space $CP^N$. They have finite energy per unit of length and contain waves propagating along vortices with the speed of light. We introduce various types of the potentials which correspond with holomorphic solutions of the integrable sector and also with several numerical solutions outside of this sector. The presented solutions constitute a strong indication that the current model contains large class of solutions with much wider range of coupling constants than the previously known exact solution.