Geometry of Solutions of Hitchin Equations on R^2
Mathematical Physics
2016-02-17 v2 math.MP
Exactly Solvable and Integrable Systems
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.
Keywords
Cite
@article{arxiv.1504.05746,
title = {Geometry of Solutions of Hitchin Equations on R^2},
author = {R. S. Ward},
journal= {arXiv preprint arXiv:1504.05746},
year = {2016}
}
Comments
13 pages, various minor changes, added references, accepted for publication in Nonlinearity