Hopf Solitons from Instanton Holonomy

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The holonomy of an SU(2) N-instanton in the x⁴-direction gives a map from R³ into SU(2), which provides a good model of an N-Skyrmion. Combining this map with the standard Hopf map from SU(2)=S³ to S² 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.