Hopf Solitons in the AFZ Model

Abstract

The Aratyn-Ferreira-Zimerman (AFZ) model is a conformal field theory in three-dimensional space. It has solutions that are topological solitons classified by an integer-valued Hopf index. There exist infinitely many axial solutions which have been found analytically. Axial, knot and linked solitons are found numerically to be static solutions using a modified volume preserving flow for Hopf index one to eight, allowing for comparison with other Hopf soliton models. Solutions include a static trefoil knot at Hopf index five. A one-parameter family of conformal Skyrme-Faddeev (CSF) models, consisting of linear combinations of the Nicole and AFZ models, are also investigated numerically. The transition of solutions for Hopf index four is mapped across these models. A topological change between linked and axial solutions occurs, with fewer models permitting axial solitons than linked solitons at Hopf index four.

17 pages, 5 figures and 2 tables

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• Dual neutral variables and knot solitons in triplet superconductors
• Knots in the Skyrme-Faddeev model
• Investigation of the Nicole model
• Hopf solitons and area preserving diffeomorphisms of the sphere
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Cited by in corpus (3)

• Topological energy bounds for the Skyrme and Faddeev models with massive pions
• Baby Skyrme models without a potential term
• Cabling in the Skyrme-Faddeev model