Mirror Symmetry, D-Branes and Counting Holomorphic Discs

Abstract

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.

31 pages

References in corpus (6)

• Phases of $N=2$ Theories In Two Dimensions
• D-Branes And Mirror Symmetry
• Open string instantons and superpotentials
• Measuring Small Distances in N=2 Sigma Models
• Mirror symmetry for open strings
• Lagrangian torus fibration and mirror symmetry of Calabi-Yau hypersurface in toric variety

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