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Mirror Symmetry, D-Branes and Counting Holomorphic Discs

2000; Cornell University; Linguagem: Inglês

10.48550/arxiv.hep-th/0012041

Mina Aganagic, Cumrun Vafa,

Algebraic Geometry and Number Theory

We consider a class of special Lagrangian subspaces of Calabi-Yau manifolds and identify their mirrors, using the recent derivation of mirror symmetry, as certain holomorphic varieties of the mirror geometry. This transforms the counting of holomorphic disc instantons ending on the Lagrangian submanifold to the classical Abel-Jacobi map on the mirror. We recover some results already anticipated as well as obtain some highly non-trivial new predictions.