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. 151191

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Abstract
We study the asymptotics of the natural L2 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 234:239403, 2013), is that on the regular part of the Hitchin system, this metric is wellapproximated 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 DumasNeitzke and later Fredrickson shows that the convergence is actually exponential.