The Ooguri-Vafa Space as a Moduli Space of Framed Wild Harmonic Bundles

Abstract

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 $\mathbb{C}{P}^1$, 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.

References in corpus (8)

• Four-dimensional wall-crossing via three-dimensional field theory
• Wall-crossing, Hitchin Systems, and the WKB Approximation
• Summing up D-Instantons
• Asymptotic behaviour of certain families of harmonic bundles on Riemann surfaces
• Gauge Theory And Wild Ramification
• Asymptotic Geometry of the Hitchin Metric
• Good Wild Harmonic Bundles and Good Filtered Higgs Bundles
• G-bundles, isomonodromy and quantum Weyl groups

Cited by in corpus (2)

• Hyperkähler metrics on the moduli space of weakly parabolic Higgs bundles
• $\mathfrak{sl}(2)$-type singular fibres of the symplectic and odd orthogonal Hitchin system