Hopf solitons on compact manifolds

Ward, R.S.

Abstract

Hopf solitons in the Skyrme-Faddeev system on R3 typically have a complicated structure, in particular when the Hopf number Q is large. By contrast, if we work on a compact 3-manifold M, and the energy functional consists only of the Skyrme term (the strong-coupling limit), then the picture simplifies. There is a topological lower bound E ≥ Q on the energy, and the local minima of E can look simple even for large Q. The aim here is to describe and investigate some of these solutions, when M is S3, T3, or S2 × S1. In addition, we review the more elementary baby-Skyrme system, with M being S2 or T2.

Citation

Ward, R. (2018). Hopf solitons on compact manifolds. Journal of Mathematical Physics, 59(2), Article 022904. https://doi.org/10.1063/1.5006891

• Journal Article Type: Article
• Acceptance Date: Feb 1, 2018
• Online Publication Date: Feb 20, 2018
• Publication Date: Feb 20, 2018
• Deposit Date: Feb 5, 2018
• Publicly Available Date: Feb 7, 2018
• Journal: Journal of Mathematical Physics
• Print ISSN: 0022-2488
• Electronic ISSN: 1089-7658
• Publisher: American Institute of Physics
• Peer Reviewed: Peer Reviewed
• Volume: 59
• Issue: 2
• Article Number: 022904
• DOI: https://doi.org/10.1063/1.5006891
• Public URL: https://durham-repository.worktribe.com/output/1367304
• Related Public URLs: https://arxiv.org/abs/1802.00657