# D-branes and Normal Functions

@article{Morrison2007DbranesAN, title={D-branes and Normal Functions}, author={David R. Morrison and Johannes Walcher}, journal={arXiv: High Energy Physics - Theory}, year={2007} }

We explain the B-model origin of extended Picard-Fuchs equations satisfied by the D-brane superpotential on compact Calabi-Yau threefolds. Via the Abel-Jacobi map, the domainwall tension is identified with a Poincare normal function--a transversal holomorphic section of the Griffiths intermediate Jacobian. Within this formalism, we derive the extended Picard-Fuchs equation associated with the mirror of the real quintic.

## 97 Citations

### Towards Open String Mirror Symmetry for One-Parameter Calabi-Yau Hypersurfaces

- Mathematics
- 2008

This work is concerned with branes and differential equations for one-parameter Calabi-Yau hypersurfaces in weighted projective spaces. For a certain class of B-branes we derive the inhomogeneous…

### Monodromy of Inhomogeneous Picard-Fuchs Equations

- Mathematics
- 2013

We study low-degree curves on one-parameter Calabi-Yau hypersurfaces, and their contribution to the space-time superpotential in a superstring compactification with D-branes. We identify all lines…

### Calculations for mirror symmetry with D-branes

- Mathematics
- 2009

We study normal functions capturing D-brane superpotentials on several one- and two-parameter Calabi-Yau hypersurfaces and complete intersections in weighted pro- jective space. We calculate in the…

### Type II/F-theory Superpotentials and Ooguri-Vafa Invariants of Compact Calabi-Yau Threefolds with Three Deformations

- Mathematics
- 2012

We calculate the D-brane superpotentials for two Calabi-Yau manifolds with three deformations by the generalized hypergeometric GKZ systems, which give rise to the flux superpotentials…

### D-brane superpotentials and Ooguri-Vafa invariants of compact Calabi-Yau threefolds

- Mathematics
- 2013

We calculate the D-brane superpotentials for two compact Calabi-Yau manifolds X14(1,1,2,3,7) and X8(1,1,1,2,3) which are of non-Fermat type in the type II string theory. By constructing the open…

### Real mirror symmetry for one-parameter hypersurfaces

- Mathematics
- 2008

We study open string mirror symmetry for one-parameter Calabi-Yau hyper- surfaces in weighted projective space. We identify mirror pairs of D-brane configurations, derive the corresponding…

### Open Topological String Amplitudes on Calabi-Yau Threefolds by Extended Holomorphic Anomaly Equation

- Mathematics
- 2022

In this paper, we study the open topological string amplitudes on Calabi-Yau threefolds by the extended holomorphic anomaly equation. The disk two-point function determined by the domainwall tension,…

### Off-shell D-brane/F-theory effective superpotentials and Ooguri Vafa invariants of several compact Calabi Yau manifolds

- Mathematics
- 2014

According to the open-closed mirror symmetry and generalized Gel'fand–Kapranov–Zelerinski (GKZ) system, we calculate off-shell D-brane/F-theory effective superpotentials of four compact Calabi–Yau…

### Another representation of the β form of the inhomogeneous Picard-Fuchs equation

- Mathematics
- 2013

In this letter we give another representation of the ? form in the inhomogeneous Picard-Fuchs equation for open topological string for some one-parameter Calabi-Yau hypersurfaces in weighted…

### D-instanton, threshold corrections, and topological string

- MathematicsJournal of High Energy Physics
- 2023

In this note, we prove that the one-loop pfaffian of the non-perturbative superpotential generated by Euclidean D-branes in type II compactifications on orientifolds of Calabi-Yau threefolds is…

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We study D-branes on the quintic CY by combining results from several directions: general results on holomorphic curves and vector bundles, stringy geometry and mirror symmetry, and the boundary…

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- Mathematics
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We show that boundary conditions in topological open string theory on Calabi–Yau (CY) manifolds are objects in the derived category of coherent sheaves, as foreseen in the homological mirror symmetry…

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We study (2,2) supersymmetric field theories on two-dimensional worldsheet with boundaries. We determine D-branes (boundary conditions and boundary interactions) that preserve half of the bulk…

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We define a particular class of topological field theories associated to open strings and prove the resulting D-branes and open strings form the bounded derived category of coherent sheaves. This…

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This is an introduction to the physics of D-branes. Topics covered include Polchinski’s original calculation, a critical assessment of some duality checks, D-brane scattering, and effective…

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We study B-type D-branes in linear sigma models with Abelian gauge groups. The most important finding is the grade restriction rule. It classifies representations of the gauge group on the Chan-Paton…

### Landau-Ginzburg to Calabi-Yau dictionary for D-branes

- Mathematics
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Based on the work by Orlov (e-print arXiv:math.AG∕0503632), we give a precise recipe for mapping between B-type D-branes in a Landau-Ginzburg orbifold model (or Gepner model) and the corresponding…

### Opening Mirror Symmetry on the Quintic

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Aided by mirror symmetry, we determine the number of holomorphic disks ending on the real Lagrangian in the quintic threefold. We hypothesize that the tension of the domainwall between the two vacua…

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A method for computing the open string mirror map and superpotential for noncompact Calabi-Yaus, following the physical computations of Lerche and Mayr, is presented. It is also shown that the…