Asymptotic Geometry of the Hitchin Metric View Full Text


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Article Info

DATE

2019-04

AUTHORS

Rafe Mazzeo, Jan Swoboda, Hartmut Weiss, Frederik Witt

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 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. More... »

PAGES

151-191

References to SciGraph publications

  • 2019-04. Asymptotics of Hitchin’s Metric on the Hitchin Section in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1987-12. Hyperkähler metrics and supersymmetry in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2009-07-20. Special geometry of Euclidean supersymmetry III: the local r-map, instantons and black holes in JOURNAL OF HIGH ENERGY PHYSICS
  • 1975-06. On the density of strebel differentials in INVENTIONES MATHEMATICAE
  • 1999-05. Special Kähler Manifolds in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2004. Complex Abelian Varieties in NONE
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    http://scigraph.springernature.com/pub.10.1007/s00220-019-03358-y

    DOI

    http://dx.doi.org/10.1007/s00220-019-03358-y

    DIMENSIONS

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