Geometry of Solutions of Hitchin Equations on R^2

Abstract

We study smooth SU(2) solutions of the Hitchin equations on R^2, with the determinant of the complex Higgs field being a polynomial of degree n. When n>=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.

13 pages, various minor changes, added references, accepted for publication in Nonlinearity

References in corpus (1)

• Nonsingular solutions of Hitchin's equations for noncompact gauge groups

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• On $2k$-Hitchin's equations and Higgs bundles: a survey
• Nonabelian Probes In Holography