The Interaction of Two Hopf Solitons

This Letter deals with topological solitons in an O(3) sigma model in three space dimensions (with a Skyrme term to stabilize their size). The solitons are classified topologically by their Hopf number N. The N=2 sector is studied; in particular, for two solitons far apart, there are three ``attractive channels’'. Viewing the solitons as dipole pairs enables one to predict the force between them. Relaxing in the attractive channels leads to various static 2-soliton solutions.