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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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Journal ArticleDOI
TL;DR: In this article, a type IIA string (or F-theory) compactified on a Calabi-Yau threefold is shown to be dual to a heterotic string on a K3 surface times a 2-torus.
Abstract: A type IIA string (or F-theory) compactified on a Calabi-Yau threefold is believed to be dual to a heterotic string on a K3 surface times a 2-torus (or on a K3 surface). We consider how the resulting moduli space of hypermultiplets is identified between these two pictures in the case of the E8 × E8 heterotic string. As examples we discuss SU(2)-bundles and G2-bundles on the K3 surface and the case of point-like instantons. We are lead to a rather beautiful identification between the integral cohomology of the Calabi-Yau threefold and some integral structures on the heterotic side somewhat reminiscent of mirror symmetry. We discuss the consequences for probing nonperturbative effects in the both the type IIA string and the heterotic string.

65 citations

Journal ArticleDOI
TL;DR: The moduli dependence of superstring compactifications based on Calabi-Yau hypersurfaces in weighted projective space has been investigated in this paper for Fermat-type polynomial constraints.
Abstract: The moduli dependence of $(2,2)$ superstring compactifications based on Calabi--Yau hypersurfaces in weighted projective space has so far only been investigated for Fermat-type polynomial constraints. These correspond to Landau-Ginzburg orbifolds with $c=9$ whose potential is a sum of $A$-type singularities. Here we consider the generalization to arbitrary quasi-homogeneous singularities at $c=9$. We use mirror symmetry to derive the dependence of the models on the complexified Kahler moduli and check the expansions of some topological correlation functions against explicit genus zero and genus one instanton calculations. As an important application we give examples of how non-algebraic (``twisted'') deformations can be mapped to algebraic ones, hence allowing us to study the full moduli space. We also study how moduli spaces can be nested in each other, thus enabling a (singular) transition from one theory to another. Following the recent work of Greene, Morrison and Strominger we show that this corresponds to black hole condensation in type II string theories compactified on Calabi-Yau manifolds.

65 citations

Journal ArticleDOI
TL;DR: In this paper, the authors use a Kaluza-Klein reduction to compute the low energy effective action for the massless modes of a spacetime-filling D6-brane wrapped on a special Lagrangian 3-cycle of a type IIA Calabi-Yau orientifold.
Abstract: We use a Kaluza-Klein reduction to compute the low-energy effective action for the massless modes of a spacetime-filling D6-brane wrapped on a special Lagrangian 3-cycle of a type IIA Calabi-Yau orientifold. The modifications to the characteristic data of the N=1 bulk orientifold theory in the presence of a D6-brane are analysed by studying the underlying Type IIA supergravity coupled to the brane worldvolume in the democratic formulation and performing a detailed dualisation procedure. The N=1 chiral coordinates are found to be in agreement with expectations from mirror symmetry. We work out the Kahler potential for the chiral superfields as well as the gauge kinetic functions for the bulk and the brane gauge multiplets including the kinetic mixing between the two. The scalar potential resulting from the dualisation procedure can be formally interpreted in terms of a superpotential. Finally, the gauging of the Peccei-Quinn shift symmetries of the complex structure multiplets reproduces the D-term potential enforcing the calibration condition for special Lagrangian 3-cycles.

65 citations

Book ChapterDOI
19 May 1992
TL;DR: Two methods for detecting symmetry in images are presented, one based directly on the intensity values and another one based on a discrete representation of local orientation, which is applied to the problem of visually guided car-following.
Abstract: We present two methods for detecting symmetry in images, one based directly on the intensity values and another one based on a discrete representation of local orientation. A symmetry finder has been developed which uses the intensity-based method to search an image for compact regions which display some degree of mirror symmetry due to intensity similarities across a straight axis. In a different approach, we look at symmetry as a bilateral relationship between local orientations. A symmetryenhancing edge detector is presented which indicates edges dependent on the orientations at two different image positions. SEED, as we call it, is a detector element implemented by a feedforward network that holds the symmetry conditions. We use SEED to find the contours of symmetric objects of which we know the axis of symmetry from the intensity-based symmetry finder. The methods presented have been applied to the problem of visually guided car-following. Real-time experiments with a system for automatic headway control on motorways have been successful.

65 citations

Posted Content
TL;DR: In this article, the Tian-Todorov theorem for the smoothness of the moduli space of Landau-Ginzburg moduli spaces is proved and the resulting families of de Rham complexes attacted to a potential are analyzed in terms of mirror symmetry.
Abstract: In this paper we prove the smoothness of the moduli space of Landau-Ginzburg models. We formulate and prove a Tian-Todorov theorem for the deformations of Landau-Ginzburg models, develop the necessary Hodge theory for varieties with potentials, and prove a double degeneration statement needed for the unobstructedness result. We discuss the various definitions of Hodge numbers for non-commutative Hodge structures of Landau-Ginzburg type and the role they play in mirror symmetry. We also interpret the resulting families of de Rham complexes attacted to a potential in terms of mirror symmetry for one parameter families of symplectic Fano manifolds and argue that modulo a natural triviality property the moduli spaces of Landau-Ginzburg models posses canonical special coordinates.

65 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202351
2022116
2021138
2020130
2019139
2018125