Hyperbolic monopoles, JNR data and spectral curves

Bolognesi, S.; Cockburn, A.; Sutcliffe, P.M.

Abstract

A large class of explicit hyperbolic monopole solutions can be obtained from JNR instanton data, if the curvature of hyperbolic space is suitably tuned. Here we provide explicit formulae for both the monopole spectral curve and its rational map in terms of JNR data. Examples with platonic symmetry are presented, together with some one-parameter families with cyclic and dihedral symmetries. These families include hyperbolic analogues of geodesics that describe symmetric monopole scatterings in Euclidean space and we illustrate the results with energy density isosurfaces. There is a metric on the moduli space of hyperbolic monopoles, defined using the Abelian connection on the boundary of hyperbolic space, and we provide a simple integral formula for this metric on the space of JNR data.

Citation

Bolognesi, S., Cockburn, A., & Sutcliffe, P. (2015). Hyperbolic monopoles, JNR data and spectral curves. Nonlinearity, 28(1), 211-235. https://doi.org/10.1088/0951-7715/28/1/211

• Journal Article Type: Article
• Acceptance Date: Nov 14, 2014
• Online Publication Date: Dec 15, 2014
• Publication Date: Jan 1, 2015
• Deposit Date: Dec 16, 2014
• Publicly Available Date: Dec 16, 2014
• Journal: Nonlinearity
• Print ISSN: 0951-7715
• Electronic ISSN: 1361-6544
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 28
• Issue: 1
• Pages: 211-235
• DOI: https://doi.org/10.1088/0951-7715/28/1/211
• Keywords: Monopoles, Spectral curves, Instantons.