Topic
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, the authors carried out the SYZ program for local Calabi-Yau manifolds of type A by developing an equivariant SYZ theory for the toric Calabi Yau manifold of infinite-type.
24 citations
TL;DR: In this paper, the leading corrections in each homology class were computed using a direct world-sheet approach without relying on any duality symmetry or supersymmetry, and the results were in perfect agreement with the earlier predictions.
Abstract: Type IIA string theory compactified on a Calabi-Yau threefold has a hypermultiplet moduli space whose metric is known to receive non-perturbative corrections from Euclidean D2-branes wrapped on 3-cycles. These corrections have been computed earlier by making use of mirror symmetry, S-duality and twistorial description of quaternionic geometries. In this paper we compute the leading corrections in each homology class using a direct world-sheet approach without relying on any duality symmetry or supersymmetry. Our results are in perfect agreement with the earlier predictions.
24 citations
TL;DR: In this article, a correspondence between the mirror symmetry of Berglund-Hubsch-Chiodo-Ruan and that for lattice polarized K3 surfaces presented by Dolgachev was shown.
Abstract: We consider K3 surfaces that possess a non-symplectic automorphism of prime order $p>2$ and we present, for these surfaces, a correspondence between the mirror symmetry of Berglund-Hubsch-Chiodo-Ruan and that for lattice polarized K3 surfaces presented by Dolgachev.
24 citations
TL;DR: In this paper, the authors study motivic zeta functions of degenerating families of Calabi-Yau varieties and show that they satisfy an analog of Igusa's monodromy conjecture if the family has a so-called Galois equivariant Kulikov model.
Abstract: We study motivic zeta functions of degenerating families of Calabi–Yau varieties. Our main result says that they satisfy an analog of Igusa’s monodromy conjecture if the family has a so-called Galois equivariant Kulikov model; we provide several classes of examples where this condition is verified. We also establish a close relation between the zeta function and the skeleton that appeared in Kontsevich and Soibelman’s non-archimedean interpretation of the SYZ conjecture in mirror symmetry.
24 citations
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TL;DR: In this paper, the authors give a survey on old and new results concerning Arnold's strange duality and show that most of the features of this duality continue to hold for the extension of it discovered by C. T. C. Wall and the author.
Abstract: We give a survey on old and new results concerning Arnold’s strange duality. We show that most of the features of this duality continue to hold for the extension of it discovered by C. T. C. Wall and the author. The results include relations to mirror symmetry and the Leech lattice.
24 citations