The Ooguri-Vafa metric, holomorphic discs and wall-crossing
Abstract
Recently, Gaiotto, Moore and Neitzke GMN08 proposed a new construction of hyperk\"ahler 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.
0