We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Durham University

Research & business

View Profile

Publication details for Paul Sutcliffe

Sutcliffe, P.M. (2007). Knots in the Skyrme-Faddeev model. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463(2087): 3001-3020.

Author(s) from Durham


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.