Torus knots as Hopfions
arXiv:1304.6021 · doi:10.1016/j.physletb.2013.12.002
Abstract
We present a direct connection between torus knots and Hopfions by finding stable and static solutions of the extended Faddeev-Skyrme model with a ferromagnetic potential term. (P,Q)--torus knots consisting of |Q| sine-Gordon kink strings twisted P/Q times into the poloidal cycle along the toroidal cycle on a toroidal domain wall carry the Hopf charge PQ, which demonstrates that Hopfions can be further classified according to torus knot type.
6 pages, 4 figures, v2: published version