Potentials and the vortex solutions in the $C{P}^N$ Skyrme-Faddeev model

Abstract

The extended Skyrme-Faddeev model possesses vortex solutions in a (3+1) dimensional Minkowski space-time with target space $C{P}^N$. 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.

12 pages, 5 figures

References in corpus (4)

• Knots in the Skyrme-Faddeev model
• Investigation of restricted baby Skyrme models
• Josephson vortices and the Atiyah-Manton construction
• Rotational symmetry breaking in baby Skyrme models

Cited by in corpus (6)

• Isolated Skyrmions in the $C{P}^2$ nonlinear $\sigma$-model with a Dzyaloshinskii-Moriya type interaction
• CP${}^2$ Skyrmions and Skyrmion Crystals in Realistic Quantum Magnets
• Compact Q-balls and Q-shells in the CPN type models
• Fractional Skyrmion molecules in a $\mathbb{C}{P}^{N-1}$ model
• Statistical nature of Skyrme-Faddeev models in $2+1$ dimensions and normalizable fermions
• Collective coordinate quantization and spin statistics of the solitons in the $\mathbb{C}{P}^N$ Skyrme-Faddeev model