Mirror Symmetry for Toric Branes on Compact Hypersurfaces
TLDR
In this article, the authors use toric geometry to study open string mirror symmetry on compact Calabi-Yau manifolds, and derive a canonical hypergeometric system of differential equations, whose solutions determine the open/closed string mirror maps and the partition functions for spheres and discs.Abstract:
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 hypergeometric system of differential equations, whose solutions determine the open/closed string mirror maps and the partition functions for spheres and discs. We define a linear sigma model for the brane geometry and describe a correspondence between dual toric polyhedra and toric brane geometries. The method is applied to study examples with obstructed and classically unobstructed brane moduli at various points in the deformation space. Computing the instanton expansion at large volume in the flat coordinates on the open/closed deformation space we obtain predictions for enumerative invariants.read more
Citations
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Computing Brane and Flux Superpotentials in F-theory Compactifications
TL;DR: In this article, the flux superpotential in F-theory compactifications with N = 1 supersymmetry is derived for all complex structure moduli including the 7-brane deformations and the field corresponding to the axio-dilaton.
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The Atiyah class and complex structure stabilization in heterotic Calabi-Yau compactifications
TL;DR: In this article, the tools necessary to use holomorphic bundles as a mechanism for moduli stabilization are systematically developed, including the Atiyah class, which determines the deformations of the complex structure for which the gauge bundle becomes non-holomorphic and hence, non-supersymmetric.
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Hints for Off-Shell Mirror Symmetry in type II/F-theory Compactifications
TL;DR: In this article, the integrability and flatness conditions of D-branes on compact Calabi-Yau manifolds in type II and F-theory compactifications were studied.
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On N=1 4d Effective Couplings for F-theory and Heterotic Vacua
TL;DR: In this article, it was shown that certain superpotential and Kahler potential couplings of N = 1 supersymmetric compactifications with branes or bundles can be computed from Hodge theory and mirror symmetry.
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The N=1 effective actions of D-branes in Type IIA and IIB orientifolds
TL;DR: In this article, the authors studied the four-dimensional N = 1 effective actions of single space-time filling D p -branes in general Type IIA and Type IIB Calabi-Yau orientifold compactifications.
References
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Phases of N = 2 theories in two dimensions
TL;DR: In this paper, a natural relation between sigma models based on Calabi-Yau hypersurfaces in weighted projective spaces and Landau-Ginzburg models is found.
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A Pair of Calabi-Yau manifolds as an exactly soluble superconformal theory
TL;DR: In this paper, the prepotentials and geometry of the moduli spaces for a Calabi-Yau manifold and its mirror were derived and all the sigma model corrections to the Yukawa couplings and moduli space metric were obtained.
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Théorie de Hodge : III
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Homological Algebra of Mirror Symmetry
TL;DR: Mirror symmetry was discovered several years ago in string theory as a duality between families of 3-dimensional Calabi-Yau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeros).