Numerical vortex solutions in (3+1) dimensions for the extended $CP^N$ Skyrme-Faddeev model

TL;DR

This paper constructs numerical vortex solutions in a (3+1)D extended $CP^N$ Skyrme-Faddeev model, demonstrating finite energy vortices with wave propagation, specifically for N=2 with charges (1,2).

Contribution

It introduces numerical vortex solutions in a non-integrable extended $CP^N$ Skyrme-Faddeev model in (3+1) dimensions, focusing on the N=2 case with specific charges.

Findings

Existence of finite energy vortex solutions with wave propagation.

Solutions characterized by charges (1,2) for N=2.

Vortices do not belong to the integrable sector.

Abstract

We construct numerical vortex solutions in a (3+1) dimensional Minkowski space-time for the extended version of the Skyrme-Faddeev model with target space $CP^N$. The solutions are essentially composed of $N$-th single vortex which does not belong to the integrable sector. They have finite energy per unit length and contain waves propagating along vortices with the speed of light. In this Letter we report on the case N=2 and show existence of the solutions with the charges $(n_1,n_2)=(1,2)$.