Winding Hopfions on R^2 x S^1

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.

22 pages, 7(+1) figures, v2: references and comments added

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• Baryonic torii: Toroidal baryons in a generalized Skyrme model
• Gauged Aloof Baby Skyrme Model
• Spacetime magnetic hopfions: from internal excitations and braiding of skyrmions
• Numerical Calculation of the Hopf Index for 3D Magnetic Textures
• Knotted instantons from annihilations of monopole-instanton complex
• Stable knots in the trapped Bose-Einstein condensates
• Steady Euler flows and the Faddeev-Skyrme model with mass term
• Instantons in Lifshitz Field Theories
• Hopf Semimetals
• Topological Soliton with Nonzero Hopf Invariant in Yang-Mills-Higgs Model