Asymptotic Geometry of the Hitchin Metric

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 et al. (Adv Math 234:239–403, 2013 ), is that on the regular part of the Hitchin system, this metric is well-approx...

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Bibliographic Details
Published in:Communications in mathematical physics 2019-04, Vol.367 (1), p.151-191
Main Authors: Mazzeo, Rafe, Swoboda, Jan, Weiss, Hartmut, Witt, Frederik
Format: Article
Language:English
Subjects:
Asymptotic properties
Classical and Quantum Gravitation
Complex Systems
Convergence
Coordinates
Mathematical analysis
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Polynomials
Quantum Physics
Relativity Theory
Theoretical
Vectors (mathematics)
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Summary: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 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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-019-03358-y