Knots in the Skyrme-Faddeev model. (English) Zbl 1133.81053

Summary: The Skyrme-Faddeev model is a modified sigma model in three-dimensional space, which has string-like topological solitons classified by the integer-valued Hopf charge. Numerical simulations are performed to compute soliton solutions for Hopf charges up to 16, with initial conditions provided by families of rational maps from the three-sphere into the complex projective line. A large number of new solutions are presented, including a variety of torus knots for a range of Hopf charges. Often these knots are only local energy minima, with the global minimum being a linked solution, but for some values of the Hopf charge they are good candidates for the global minimum energy solution. The computed energies are in agreement with Ward’s conjectured energy bound.


81T10 Model quantum field theories
35Q51 Soliton equations
57M25 Knots and links in the \(3\)-sphere (MSC2010)
Full Text: DOI arXiv


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