Knots in the Skyrme-Faddeev model

Understand

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.