The Ooguri-Vafa metric, holomorphic discs and wall-crossing
Kwokwai Chan
TL;DR
This paper interprets formulas from the Gaiotto-Moore-Neitzke construction of the Ooguri-Vafa metric as wall-crossing formulas, highlighting their connection to holomorphic discs in the context of mirror symmetry and special Lagrangian fibrations.
Contribution
It establishes a novel interpretation of the Ooguri-Vafa metric formulas as wall-crossing phenomena related to holomorphic discs in mirror symmetry.
Findings
Formulas from GMN construction are wall-crossing formulas.
Connection between Ooguri-Vafa metric and holomorphic discs.
Insights into instanton corrections in mirror symmetry.
Abstract
Recently, Gaiotto, Moore and Neitzke \cite{GMN08} proposed a new construction of hyperk\"{a}hler metrics. In particular, they gave a new construction of the Ooguri-Vafa metric, in which they came across certain formulas. We interpret those formulas as wall-crossing formulas that appear in the SYZ construction of instanton-corrected mirror manifolds. This reveals the close relation between the Ooguri-Vafa metric and nontrivial holomorphic discs with boundary in special Lagrangian torus fibers.
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