On N=1 Mirror Symmetry for Open Type II Strings

Abstract

We study the open string extension of the mirror map for N=1 supersymmetric type II vacua with D-branes on non-compact Calabi-Yau manifolds. Its definition is given in terms of a system of differential equations that annihilate certain period and chain integrals. The solutions describe the flat coordinates on the N=1 parameter space, and the exact disc instanton corrected superpotential on the D-brane world-volume. A gauged linear sigma model for the combined open-closed string system is also given. It allows to use methods of toric geometry to describe D-brane phase transitions and the N=1 Kähler cone. Applications to a variety of D-brane geometries are described in some detail.

harvmac, 35 pages (b), 2 figures; v2: typos & references corrected

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Cited by in corpus (45)

• Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes
• Open string amplitudes and large order behavior in topological string theory
• The effective action of D7-branes in N=1 Calabi-Yau orientifolds
• Orientifolds of K3 and Calabi-Yau Manifolds with Intersecting D-branes
• D-terms and F-terms from D7-brane fluxes
• RR photons
• F-theory Flux, Destabilization of Orientifolds and Soft Terms on D7--Branes
• Orientifolds, Mirror Symmetry and Superpotentials
• N=1 Special Geometry, Mixed Hodge Variations and Toric Geometry
• Hints for Off-Shell Mirror Symmetry in type II/F-theory Compactifications
• Holomorphic N=1 Special Geometry of Open--Closed Type II Strings
• D-branes on Calabi-Yau Manifolds and Superpotentials
• The effective action of D6-branes in N=1 type IIA orientifolds
• D-brane superpotentials and RG flows on the quintic
• Five-Brane Superpotentials and Heterotic/F-theory Duality
• Relative periods and open-string integer invariants for a compact Calabi-Yau hypersurface
• On N=1 4d Effective Couplings for F-theory and Heterotic Vacua
• Calculations for Mirror Symmetry with D-branes
• The Geometry of D-Brane Superpotentials
• The effective action of D-branes in Calabi-Yau orientifold compactifications
• Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds
• Crepant resolutions and open strings
• Open Gromov-Witten invariants, mirror maps, and Seidel representations for toric manifolds
• Open topological strings and integrable hierarchies: Remodeling the A-model
• Summing up Open String Instantons and N=1 String Amplitudes
• On the Open-Closed B-Model
• D-brane Superpotentials: Geometric and Worldsheet Approaches
• Orientifolds, Unoriented Instantons and Localization
• Moduli Webs and Superpotentials for Five-Branes
• Integrality theorems in the theory of topological strings
• Special Geometry and Mirror Symmetry for Open String Backgrounds with N=1 Supersymmetry
• A Note on Computations of D-brane Superpotential
• D-Branes in Topological String Theory
• Holomorphic Couplings In Non-Perturbative String Compactifications
• Local B-model Yukawa couplings from A-twisted correlators
• A Geometrical Construction of Rational Boundary States in Linear Sigma Models
• Reconstructing GKZ via topological recursion
• Counting BPS States via Holomorphic Anomaly Equations
• Some integrality properties in local mirror symmetry
• Topological open string amplitudes on local toric del Pezzo surfaces via remodeling the B-model
• Log BPS numbers of log Calabi-Yau surfaces
• Open Mirror Symmetry for Higher Dimensional Calabi-Yau Hypersurfaces
• Integrality Properties of Open-Closed Mirror Maps
• Quantum McKay correspondence for disc invariants of toric Calabi-Yau 3-orbifolds
• GKZ Hypergeometric Series for the Hesse Pencil, Chain Integrals and Orbifold Singularities