The Ooguri-Vafa metric, holomorphic discs and wall-crossing
Symplectic Geometry
2014-02-19 v4 Differential Geometry
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.
Keywords
Cite
@article{arxiv.0909.3608,
title = {The Ooguri-Vafa metric, holomorphic discs and wall-crossing},
author = {Kwokwai Chan},
journal= {arXiv preprint arXiv:0909.3608},
year = {2014}
}
Comments
v4: 14 pages, improved exposition