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

• Autores: Kwokwai Chan
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 17, Nº 2-3, 2010, págs. 401-414
• Idioma: inglés
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• Resumen

  • 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.