Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 21 (2025), 005, 63 pages      arXiv:1912.00261      https://doi.org/10.3842/SIGMA.2025.005

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

Iván Tulli
Department of Pure Mathematics, University of Sheffield, Sheffield, S3 7RH, UK

Received April 08, 2024, in final form January 05, 2025; Published online January 14, 2025

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.

Key words: Higgs bundles; hyperkähler geometry; twistor spaces; Stokes data.

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