The Geometry of D-Brane Superpotentials
arXiv:0909.2245 · doi:10.1007/JHEP12(2011)060
Abstract
The disk partition function of the open topological string computes the spacetime superpotential for D-branes wrapping cycles of a compact Calabi-Yau threefold. We use string duality to show that when appropriately formulated, the problem admits a natural geometrization in terms of a non-compact Calabi-Yau fourfold without D-branes. The duality relates the D-brane superpotential to a flux superpotential on the fourfold. This sheds light on several features of superpotential computations appearing in the literature, in particular on the observation that Calabi-Yau fourfold geometry enters the problem. In one of our examples, we show that the geometry of fourfolds also reproduces the D-brane superpotentials obtained from matrix factorization methods.
v2: 30 pages, harvmac; appendix added, reference added, typos corrected
References in corpus (12)
- Les Houches Lectures on Constructing String Vacua
- D-brane Deconstructions in IIB Orientifolds
- N=1 Special Geometry, Mixed Hodge Variations and Toric Geometry
- Hints for Off-Shell Mirror Symmetry in type II/F-theory Compactifications
- Computing Brane and Flux Superpotentials in F-theory Compactifications
- Opening Mirror Symmetry on the Quintic
- Holomorphic N=1 Special Geometry of Open--Closed Type II Strings
- Relative periods and open-string integer invariants for a compact Calabi-Yau hypersurface
- D-branes and Normal Functions
- Calculations for Mirror Symmetry with D-branes
- Mirror Symmetry for Toric Branes on Compact Hypersurfaces
- Gromov-Witten/Donaldson-Thomas correspondence for toric 3-folds
Cited by in corpus (28)
- Lectures on F-theory compactifications and model building
- G-flux in F-theory and algebraic cycles
- Hints for Off-Shell Mirror Symmetry in type II/F-theory Compactifications
- Five-Brane Superpotentials and Heterotic/F-theory Duality
- On N=1 4d Effective Couplings for F-theory and Heterotic Vacua
- TASI lectures on complex structures
- Type II/F-theory Superpotentials with Several Deformations and N=1 Mirror Symmetry
- Quivers from Matrix Factorizations
- Fluxbrane Inflation
- D-brane Superpotentials: Geometric and Worldsheet Approaches
- Open mirror symmetry for Pfaffian Calabi-Yau 3-folds
- Stable maps to Looijenga pairs
- D7-Brane Moduli vs. F-Theory Cycles in Elliptically Fibred Threefolds
- A Note on Computations of D-brane Superpotential
- Picard-Fuchs Equations for Relative Periods and Abel-Jacobi Map for Calabi-Yau Hypersurfaces
- Holomorphic Couplings In Non-Perturbative String Compactifications
- Weak Coupling, Degeneration and Log Calabi-Yau Spaces
- Remarks on quiver gauge theories from open topological string theory
- Manifestly Supersymmetric RG Flows
- Flat Connections in Open String Mirror Symmetry
- On the Arithmetic of D-brane Superpotentials. Lines and Conics on the Mirror Quintic
- D-brane Moduli Spaces and Superpotentials in a Two-Parameter Model
- Reflections of NS5 branes
- Mirror Symmetry, D-brane Superpotential and Ooguri-Vafa Invariants of Compact Calabi-Yau Manifolds
- 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