Knots in the Skyrme-Faddeev model

Details Knots in the Skyrme-Faddeev model Knots in the Skyrme-Faddeev model

2007-05-10

arxiv.org/abs/0705.1468v1

Proc.Roy.Soc.Lond.A463:3001-3020,2007

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, 5 figures

Scientific paper

10.1098/rspa.2007.0038

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 sixteen, 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.

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