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Mirror symmetry
About: Mirror symmetry is a research topic. Over the lifetime, 2422 publications have been published within this topic receiving 90786 citations.
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TL;DR: In this paper, a progress in obtaining the complete nonperturbative effective action of type II string theory compactified on a Calabi-Yau manifold is reported. But the authors do not consider the quantum corrections to the metric on the hypermultiplet moduli space.
75 citations
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TL;DR: In this paper, the authors use local mirror symmetry in type IIA string compactifications on Calabi-Yau n+1 folds to construct vector bundles on (possibly singular) elliptically fibered Calabi Yau n-folds Z_n.
Abstract: We use local mirror symmetry in type IIA string compactifications on Calabi-Yau n+1 folds $X_{n+1}$ to construct vector bundles on (possibly singular) elliptically fibered Calabi-Yau n-folds Z_n. The interpretation of these data as valid classical solutions of the heterotic string compactified on Z_n proves F-theory/heterotic duality at the classical level. Toric geometry is used to establish a systematic dictionary that assigns to each given toric n+1-fold $X_{n+1}$ a toric n fold Z_n together with a specific family of sheafs on it. This allows for a systematic construction of phenomenologically interesting d=4 N=1 heterotic vacua, e.g. on deformations of the tangent bundle, with grand unified and SU(3)\times SU(2) gauge groups. As another application we find non-perturbative gauge enhancements of the heterotic string on singular Calabi-Yau manifolds and new non-perturbative dualities relating heterotic compactifications on different manifolds.
74 citations
TL;DR: In this paper, the authors consider a localization construction which appears, at least conjecturally, in symplectic geometry, and they consider a specific example, coming from mirror symmetry, which they call mirror-symmetric localization.
Abstract: We consider a localization construction which appears, at least conjecturally, in symplectic geometry. Besides the general algebraic theory, we also look at a specific example, coming from mirror symmetry.
73 citations
TL;DR: In this article, the Strominger-Yau-Zaslow mirror transformation is applied to understand the geometry of the mirror symmetry between toric Fano manifolds and Landau-Ginzburg models.
73 citations
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TL;DR: In this article, a large class of maximally degenerating families of n-dimensional polarized varieties are obtained by smoothing a reducible union of toric varieties governed by a wall structure on a real n-pseudo-manifold.
Abstract: We show that a large class of maximally degenerating families of n-dimensional polarized varieties come with a canonical basis of sections of powers of the ample line bundle. The families considered are obtained by smoothing a reducible union of toric varieties governed by a wall structure on a real n-(pseudo-)manifold. Wall structures have previously been constructed inductively for cases with locally rigid singularities and by Gromov-Witten theory for mirrors of log Calabi-Yau surfaces and K3 surfaces by various combinations of the authors. For trivial wall structures on the n-torus we retrieve the classical theta functions. Possible applications include mirror symmetry, geometric compactifications of moduli of certain polarized varieties via stable pairs and geometric quantization.
73 citations