Geometry of Solutions of Hitchin Equations on R^2

Ward, R.S.

Abstract

We study smooth SU(2) solutions of the Hitchin equations on ${{\mathbb{R}}^{2}}$ , with the determinant of the complex Higgs field being a polynomial of degree n. When $n\geqslant 3$ , there are moduli spaces of solutions, in the sense that the natural L 2 metric is well-defined on a subset of the parameter space. We examine rotationally-symmetric solutions for n  =  1 and n  =  2, and then focus on the n  =  3 case, elucidating the moduli and describing the asymptotic geometry as well as the geometry of two totally-geodesic surfaces.

Citation

Ward, R. (2016). Geometry of Solutions of Hitchin Equations on R^2. Nonlinearity, 29(3), Article 756. https://doi.org/10.1088/0951-7715/29/3/756

• Journal Article Type: Article
• Acceptance Date: Jan 5, 2016
• Online Publication Date: Jan 25, 2016
• Publication Date: Jan 1, 2016
• Deposit Date: Jan 5, 2016
• Publicly Available Date: Jan 25, 2017
• Journal: Nonlinearity
• Print ISSN: 0951-7715
• Electronic ISSN: 1361-6544
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 29
• Issue: 3
• Article Number: 756
• DOI: https://doi.org/10.1088/0951-7715/29/3/756
• Public URL: https://durham-repository.worktribe.com/output/1415691
• Related Public URLs: http://arxiv.org/abs/1504.05746