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      Calabi-Yau manifolds and sporadic groups

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          Abstract

          A few years ago a connection between the elliptic genus of the K3 manifold and the largest Mathieu group M\(_{24}\) was proposed. We study the elliptic genera for Calabi-Yau manifolds of larger dimensions and discuss potential connections between the expansion coefficients of these elliptic genera and sporadic groups. While the Calabi-Yau 3-fold case is rather uninteresting, the elliptic genera of certain Calabi-Yau \(d\)-folds for \(d>3\) have expansions that could potentially arise from underlying sporadic symmetry groups. We explore such potential connections by calculating twined elliptic genera for a large number of Calabi-Yau 5-folds that are hypersurfaces in weighted projected spaces, for a toroidal orbifold and two Gepner models.

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          Elliptic genera and quantum field theory

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            Finite groups of automorphisms of K3 surfaces and the Mathieur group

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              On the Landau-Ginzburg Description of \(N=2\) Minimal Models

              (2010)
              The conjecture that \(N=2\) minimal models in two dimensions are critical points of a super-renormalizable Landau-Ginzburg model can be tested by computing the path integral of the Landau-Ginzburg model with certain twisted boundary conditions. This leads to simple expressions for certain characters of the \(N=2\) models which can be verified at least at low levels. An \(N=2\) superconformal algebra can in fact be found directly in the {\it noncritical} Landau-Ginzburg system, giving further support for the conjecture.
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                Author and article information

                Journal
                27 November 2017
                Article
                1711.09698
                dea9f5ec-9d43-4f80-9832-ecfec5c3c0e4

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                34 pages
                hep-th

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