The Ooguri-Vafa metric, holomorphic discs and wall-crossing

Details The Ooguri-Vafa metric, holomorphic discs and wall-crossing The Ooguri-Vafa metric, holomorphic discs and wall-crossing

2009-09-19

arxiv.org/abs/0909.3608v4

Math. Res. Lett. 17 (2010), no. 3, 401-414

Mathematics

Symplectic Geometry

v4: 14 pages, improved exposition

Scientific paper

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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