Hopf Solitons from Instanton Holonomy

TL;DR

This paper explores how instanton holonomy can be used to model Hopf solitons in the Skyrme-Faddeev framework, focusing on single and two-soliton configurations and their interactions.

Contribution

It introduces a novel approach to approximate Hopf solitons using instanton holonomy, providing insights into soliton interactions and configurations.

Findings

Instanton holonomy effectively models N=1 and N=2 Hopf solitons.

The approach offers a new perspective on soliton interactions.

Approximate solutions align with known properties of Hopf solitons.

Abstract

The holonomy of an SU(2) N-instanton in the x^4-direction gives a map from R^3 into SU(2), which provides a good model of an N-Skyrmion. Combining this map with the standard Hopf map from SU(2)=S^3 to S^2 gives a configuration for a Hopf soliton of charge N. In this way, one may define a collective-coordinate manifold for Hopf solitons. This paper deals with instanton approximations to Hopf solitons in the Skyrme-Faddeev model, focussing in particular on the N=1 and N=2 sectors, and the two-soliton interaction.