The Ooguri-Vafa space as a moduli space of framed wild harmonic bundles
arxiv(2019)
摘要
The Ooguri-Vafa space is a 4-dimensional incomplete hyperkähler manifold,
defined on the total space of a singular torus fibration with one singular
nodal fiber. It has been proposed that the Ooguri-Vafa hyperkähler metric
should be part of the local model of the hyperkähler metric of the Hitchin
moduli spaces, near the most generic kind of singular locus of the Hitchin
fibration. In order to relate the Ooguri-Vafa space with the Hitchin moduli
spaces, we show that the Ooguri-Vafa space can be interpreted as a set of rank
2, framed wild harmonic bundles over ℂP^1, with one irregular
singularity. Along the way we show that a certain twistor family of holomorphic
Darboux coordinates, which describes the hyperkähler geometry of the
Ooguri-Vafa space, has an interpretation in terms of Stokes data associated to
our framed wild harmonic bundles.
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