Asymptotic Geometry of the Hitchin Metric

Mazzeo, Rafe; Swoboda, Jan; Weiss, Hartmut; Witt, Frederik (2019): Asymptotic Geometry of the Hitchin Metric. In: Communications in Mathematical Physics, Vol. 367, No. 1: pp. 151-191

Abstract

We study the asymptotics of the natural L-2 metric on the Hitchin moduli space with group G=SU(2). Our main result, which addresses a detailed conjectural picture made by Gaiotto etal. (Adv Math 234:239-403, 2013), is that on the regular part of the Hitchin system, this metric is well-approximated by the semiflat metric from Gaiotto et al. (2013). We prove that the asymptotic rate of convergence for gauged tangent vectors to the moduli space has a precise polynomial expansion, and hence that the difference between the two sets of metric coefficients in a certain natural coordinate system also has polynomial decay. New work by Dumas-Neitzke and later Fredrickson shows that the convergence is actually exponential.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0010-3616
• Language: English