# Calculations for mirror symmetry with D-branes

@article{Walcher2009CalculationsFM, title={Calculations for mirror symmetry with D-branes}, author={Johannes Walcher}, journal={Journal of High Energy Physics}, year={2009}, volume={2009}, pages={129-129} }

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 B-model and interpret the results using mirror symmetry in the large volume regime, albeit without identifying the precise A-model geometry in all cases. We identify new classes of extensions of Picard-Fuchs equations, as well as a novel type of topology changing phase transition involving quantum D…

## 35 Citations

The geometry of D-brane superpotentials

- Mathematics
- 2011

A bstractThe 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…

Mirror symmetry, D-brane superpotentials and Ooguri-Vafa invariants of Calabi-Yau manifolds

- Mathematics
- 2015

The D-brane superpotential is very important in the low energy effective theory. As the generating function of all disk instantons from the worldsheet point of view, it plays a crucial role in…

Five-brane superpotentials, blow-up geometries and SU(3) structure manifolds

- Mathematics
- 2011

We investigate the dynamics of space-time filling five-branes wrapped on curves in heterotic and orientifold Calabi-Yau compactifications. We first study the leading $ \mathcal{N} = 1 $ scalar…

A note on computations of the D-brane superpotential

- Mathematics
- 2011

We develop some computational methods for the integrals over the 3-chains on the compact Calabi–Yau 3-folds that play a prominent role in the analysis of the topological B-model in the context of the…

Type II/F-theory superpotentials with several deformations and $ \mathcal{N} = 1 $ mirror symmetry

- Mathematics
- 2010

We present a detailed study of D-brane superpotentials depending on several open and closed-string deformations. The relative cohomology group associated with the brane defines a generalized…

Flat connections in open string mirror symmetry

- Mathematics
- 2012

A bstractWe study a flat connection defined on the open-closed deformation space of open string mirror symmetry for type II compactifications on Calabi-Yau threefolds with D-branes. We use flatness…

Open mirror symmetry for higher dimensional Calabi-Yau hypersurfaces

- Mathematics
- 2015

A bstractCompactifications with fluxes and branes motivate us to study various enumerative invariants of Calabi-Yau manifolds. In this paper, we study non-perturbative corrections depending on both…

## References

SHOWING 1-10 OF 49 REFERENCES

On N=1 Mirror Symmetry for Open Type II Strings

- Mathematics
- 2001

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…

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…

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…

Opening Mirror Symmetry on the Quintic

- Mathematics
- 2006

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…

Phases Of N=2 Theories In 1+1 Dimensions With Boundary

- Mathematics
- 2008

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…

Computation of Superpotentials for D-Branes

- Mathematics
- 2006

We present a general method for the computation of tree-level superpotentials for the world-volume theory of B-type D-branes. This includes quiver gauge theories in the case that the D-brane is…

Evidence for Tadpole Cancellation in the Topological String

- Mathematics
- 2007

We study the topological string on compact Calabi-Yau threefolds in the presence of orientifolds and D-branes. In examples, we find that the total topological string amplitude admits a BPS expansion…

Disk Instantons, Mirror Symmetry and the Duality Web

- Mathematics
- 2002

We apply the methods recently developed for computation of type IIA disk instantons using mirror symmetry to a large class of D-branes wrapped over Lagrangian cycles of non-compact Calabi-Yau…

Mirror symmetry for toric branes on compact hypersurfaces

- Mathematics
- 2009

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…