The Interaction of Two Hopf Solitons

TL;DR

This paper investigates the interactions of Hopf solitons in an O(3) sigma model, analyzing their topological classification, attractive channels, and resulting static solutions, with insights into their force predictions and configurations.

Contribution

It introduces a detailed analysis of two Hopf solitons' interactions, including force predictions and static configurations, within a stabilized O(3) sigma model.

Findings

Identification of three attractive channels for two solitons

Prediction of forces based on dipole pair models

Construction of various static 2-soliton solutions

Abstract

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.