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
References in corpus (14)
- Reconfigurable knots and links in chiral nematic colloids
- Stationary ring solitons in field theory - knots and vortons
- Josephson vortices and the Atiyah-Manton construction
- Matryoshka Skyrmions
- Jewels on a wall ring
- Vortex rings in ferromagnets
- Massive Hopfions
- Isospinning hopfions
- Classically Isospinning Hopf Solitons
- Walls and chains of planar skyrmions
- Instantons confined by monopole strings
- Knots from wall--anti-wall annihilations with stretched strings
- Toroidal domain walls as Hopfions
- Knotted domain strings
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- Magnetic Hopfions in the Faddeev-Skyrme-Maxwell model
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