Exponential Decay for the Asymptotic Geometry of the Hitchin Metric

Abstract

We consider Hitchin's hyperkähler metric $g_{L^2}$ on the $SU(n)$-Hitchin moduli space moduli space over a compact Riemann surface. We prove that the difference between the metric $g_{L^2}$ and a simpler "semiflat" hyperkähler metric $g_{\mathrm{sf}}$ is exponentially-decaying along generic rays in the Hitchin moduli space, as conjectured by Gaiotto-Moore-Neitzke.

arXiv comment37 pages

References in corpus (5)

• Four-dimensional wall-crossing via three-dimensional field theory
• Special Kahler Manifolds
• Ends of the moduli space of Higgs bundles
• Asymptotic Geometry of the Hitchin Metric
• Asymptotics of Hitchin's metric on the Hitchin section

Cited by in corpus (6)

• Higgs bundles, harmonic maps, and pleated surfaces
• The Algebraic and Analytic Compactifications of the Hitchin Moduli Space
• Seiberg-Witten differentials on the Hitchin base
• Nilpotent Higgs bundles and families of flat connections
• Interpreting the Ooguri-Vafa symplectic form à la Atiyah-Bott
• Special Joyce structures and hyperkähler metrics