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

Abstract

Recently, Gaiotto, Moore and Neitzke \cite{GMN08} proposed a new construction of hyperkähler 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.

v4: 14 pages, improved exposition

References in corpus (2)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Mirror symmetry and T-duality in the complement of an anticanonical divisor

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