Special Geometry and Mirror Symmetry for Open String Backgrounds with N=1 Supersymmetry

Abstract

We review an approach for computing non-perturbative, exact superpotentials for Type II strings compactified on Calabi-Yau manifolds, with extra fluxes and D-branes on top. The method is based on an open string generalization of mirror symmetry, and takes care of the relevant sphere and disk instanton contributions. We formulate a framework based on relative (co)homology that uniformly treats the flux and brane sectors on a similar footing. However, one important difference is that the brane induced potentials are of much larger functional diversity than the flux induced ones, which have a hidden N=2 structure and depend only on the bulk geometry. This introductory lecture is meant for an audience unfamiliar with mirror symmetry.

latex, 35p, 2 figs, refs added; brief comments about duality to fourfolds added in the concluding section

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Cited by in corpus (9)

• Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes
• Hints for Off-Shell Mirror Symmetry in type II/F-theory Compactifications
• The effective action of D6-branes in N=1 type IIA orientifolds
• The effective action of D-branes in Calabi-Yau orientifold compactifications
• On D-brane moduli stabilisation
• Integrality theorems in the theory of topological strings
• Special geometry of local Calabi-Yau manifolds and superpotentials from holomorphic matrix models
• A Note on Computations of D-brane Superpotential
• Supersymmetric Gauge Theories from String Theory