Winding Hopfions on R^2 x S^1

TL;DR

This paper investigates winding Hopfions in the Faddeev-Skyrme model on R^2 x S^1, revealing new stable solutions with twisted U(1) moduli and analyzing their properties under different potential terms.

Contribution

It introduces and numerically constructs winding Hopfions with twisted U(1) moduli in the Faddeev-Skyrme model on R^2 x S^1, expanding understanding of topological solitons.

Findings

Existence of stable winding Hopfions with Hopf charge PQ.

Numerical solutions for potential linear and ferromagnetic potentials.

Q-lump carries unit Hopf charge per period in 2+1 dimensions.

Abstract

We study Hopfions in the Faddeev-Skyrme model with potential terms on R^2 x S^1. Apart from the conventional Hopfions, there exist winding Hopfions, that is, the lump (baby Skyrmion) strings with the lump charge Q with the U(1) modulus twisted P times along S^1, having the Hopf charge PQ. We consider two kinds of potential terms, that is, the potential linear in the field and the ferromagnetic potential with two easy axes, and present stable solutions numerically. We also point out that a Q-lump carries the unit Hopf charge per the period in d=2+1.