Mirror Symmetry for Toric Branes on Compact Hypersurfaces

Abstract

We use toric geometry to study open string mirror symmetry on compact Calabi-Yau manifolds. For a mirror pair of toric branes on a mirror pair of toric hypersurfaces we derive a canonical hypergeometric system of differential equations, whose solutions determine the open/closed string mirror maps and the partition functions for spheres and discs. We define a linear sigma model for the brane geometry and describe a correspondence between dual toric polyhedra and toric brane geometries. The method is applied to study examples with obstructed and classically unobstructed brane moduli at various points in the deformation space. Computing the instanton expansion at large volume in the flat coordinates on the open/closed deformation space we obtain predictions for enumerative invariants.

36 pages, references added

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Cited by in corpus (26)

• G-flux in F-theory and algebraic cycles
• The Atiyah Class and Complex Structure Stabilization in Heterotic Calabi-Yau Compactifications
• Computing Brane and Flux Superpotentials in F-theory Compactifications
• The N=1 effective actions of D-branes in Type IIA and IIB orientifolds
• The Geometry of D-Brane Superpotentials
• Type II/F-theory Superpotentials with Several Deformations and N=1 Mirror Symmetry
• Fluxbrane Inflation
• D-brane Superpotentials: Geometric and Worldsheet Approaches
• Effective action from M-theory on twisted connected sum $G_2$-manifolds
• Dual Pairs of Gauged Linear Sigma Models and Derived Equivalences of Calabi-Yau threefolds
• Open mirror symmetry for Pfaffian Calabi-Yau 3-folds
• Five-Brane Superpotentials, Blow-Up Geometries and SU(3) Structure Manifolds
• D7-Brane Moduli vs. F-Theory Cycles in Elliptically Fibred Threefolds
• Holomorphic Couplings In Non-Perturbative String Compactifications
• Comments on M${}_{24}$ representations and $C{Y}_3$ geometries
• Remarks on quiver gauge theories from open topological string theory
• Manifestly Supersymmetric RG Flows
• Off-shell D-Brane/F-Theory Effective Superpotentials and Ooguri-Vafa Invariants of Several Compact Calabi-Yau Manifolds
• Flat Connections in Open String Mirror Symmetry
• D-brane Moduli Spaces and Superpotentials in a Two-Parameter Model
• Open Mirror Symmetry for Higher Dimensional Calabi-Yau Hypersurfaces
• Effective Superpotentials of Type II D-brane/F-theory on Compact Complete Intersection Calabi-Yau Threefolds
• Ooguri-Vafa Invariants and Off-shell Superpotentials of Type II/F-theory compactification
• Bulk deformations of open topological string theory
• Superpotentials of D-branes in Calabi-Yau Manifolds with Several Moduli by Mirror Symmetry and Blown-up
• The Number of Rational Points of Two Parameter Calabi-Yau manifolds as Toric Hypersurfaces