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.