Cyclic Higgs bundles and the affine Toda equations

Abstract

We introduce a class of Higgs bundles called cyclic which lie in the Hitchin component of representations of a compact Riemann surface into the split real form of a simple Lie group. We then prove that such a Higgs bundle is equivalent to a certain class of solutions to the affine Toda equations. We further explain this relationships in terms of lifts of harmonic maps.

23 pages

References in corpus (2)

• Holomorphic Curves and Toda Systems
• Geometry of Higgs and Toda Fields on Riemann Surfaces

Cited by in corpus (11)

• Asymptotics of certain families of Higgs bundles in the Hitchin component
• An Introduction to Higgs Bundles via Harmonic Maps
• Maximal Sp(4,R) surface group representations, minimal immersions and cyclic surfaces
• Generalized Kazdan-Warner equations associated with a linear action of a torus on a complex vector space
• Correlation of the renormalized Hilbert length for convex projective surfaces
• Twisted cyclic quiver varieties on curves
• The Asymptotics of Representations for Cyclic Opers
• Cyclic Higgs bundles and the Toledo invariant
• On diagonal pluriharmonic metrics of $G$-Higgs bundles
• The geometric Toda equations for noncompact symmetric spaces
• Higher Complex Structures and Higher Teichmüller Theory