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 article, it was shown that the elliptic genus of a Calabi-Yau manifold is a Jacobi form, and that the dimensions of the genus can be determined by the Hodge numbers.
Abstract: The paper contains a proof that elliptic genus of a Calabi-Yau manifold is a Jacobi form, finds in which dimensions the elliptic genus is determined by the Hodge numbers and shows that elliptic genera of a Calabi-Yau hypersurface in a toric variety and its mirror coincide up to sign. The proof of the mirror property is based on the extension of elliptic genus to Calabi-Yau hypersurfaces in toric varieties with Gorenstein singularities.
67 citations
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TL;DR: The integral cohomology groups for all examples of Calabi-Yau 3-folds obtained from hypersurfaces in 4-dimensional Gorenstein toric Fano varieties were derived in this paper.
Abstract: In this paper, we compute the integral cohomology groups for all examples of Calabi-Yau 3-folds obtained from hypersurfaces in 4-dimensional Gorenstein toric Fano varieties. Among 473 800 776 families of Calabi-Yau 3-folds $X$ corresponding to 4-dimensional reflexive polytopes there exist exactly 32 families having non-trivial torsion in $H^*(X, \Z)$. We came to an interesting observation that the torsion subgroups in $H^2$ and $H^3$ are exchanged by the mirror symmetry involution, i.e. the torsion subgroup in the Picard group of $X$ is isomorphic to the Brauer group of the mirror $X^*$
66 citations
TL;DR: In this article, the T-duality/mirror transformation in Calabi-Yau spaces was extended to the case of spin(7) holonomy, and it was shown that manifolds of G2 holonomy which have a mirror of the first (second) type admit supersymmetric T3 (T4) fibrations.
66 citations
TL;DR: In this article, open string mirror symmetry for one-parameter Calabi-Yau hyper- surfaces in weighted projective space was studied and the corresponding Picard-Fuchs equations were derived.
Abstract: 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 inhomogeneous Picard-Fuchs equations, and solve for the do- mainwall tensions as analytic functions over moduli space. Our calculations exemplify several features that had not been seen in previous work on the quintic or local Calabi-Yau manifolds. We comment on the calculation of loop amplitudes.
66 citations
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TL;DR: In this paper, it was shown that the information encoded in the quantum periods is radically insufficient to determine the spectrum: there is an infinite series of instanton corrections, which are non-perturbative in \hbar, and lead to an exact WKB quantization condition.
Abstract: We study a spectral problem associated to the quantization of a spectral curve arising in local mirror symmetry. The perturbative WKB quantization condition is determined by the quantum periods, or equivalently by the refined topological string in the Nekrasov-Shatashvili (NS) limit. We show that the information encoded in the quantum periods is radically insufficient to determine the spectrum: there is an infinite series of instanton corrections, which are non-perturbative in \hbar, and lead to an exact WKB quantization condition. Moreover, we conjecture the precise form of the instanton corrections: they are determined by the standard or un-refined topological string free energy, and we test our conjecture successfully against numerical calculations of the spectrum. This suggests that the non-perturbative sector of the NS refined topological string contains information about the standard topological string. As an application of the WKB quantization condition, we explain some recent observations relating membrane instanton corrections in ABJM theory to the refined topological string.
65 citations