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Communications in Mathematical Physics

, Volume 367, Issue 1, pp 151–191 | Cite as

Asymptotic Geometry of the Hitchin Metric

  • Rafe MazzeoEmail author
  • Jan Swoboda
  • Hartmut Weiss
  • Frederik Witt
Article
  • 55 Downloads

Abstract

We study the asymptotics of the natural L2 metric on the Hitchin moduli space with group \({G = \mathrm{SU}(2)}\). Our main result, which addresses a detailed conjectural picture made by Gaiotto et al. (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.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsStanford UniversityStanfordUSA
  2. 2.Mathematisches Institut der Universität MünchenMunichGermany
  3. 3.Mathematisches Seminar der Universität KielKielGermany
  4. 4.Institut für Geometrie und Topologie der Universität StuttgartStuttgartGermany

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