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      Mathieu Moonshine and Orbifold K3s

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          Abstract

          The current status of `Mathieu Moonshine', the idea that the Mathieu group M24 organises the elliptic genus of K3, is reviewed. While there is a consistent decomposition of all Fourier coefficients of the elliptic genus in terms of Mathieu M24 representations, a conceptual understanding of this phenomenon in terms of K3 sigma-models is still missing. In particular, it follows from the recent classification of the automorphism groups of arbitrary K3 sigma-models that (i) there is no single K3 sigma-model that has M24 as an automorphism group; and (ii) there exist `exceptional' K3 sigma-models whose automorphism group is not even a subgroup of M24. Here we show that all cyclic torus orbifolds are exceptional in this sense, and that almost all of the exceptional cases are realised as cyclic torus orbifolds. We also provide an explicit construction of a Z5 torus orbifold that realises one exceptional class of K3 sigma-models.

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          Most cited references6

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          Vertex algebras, Kac-Moody algebras, and the Monster

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            Finite groups of automorphisms of K3 surfaces and the Mathieur group

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              Calculus of twisted vertex operators

              J Lepowsky (1985)
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                Author and article information

                Journal
                1206.5143

                High energy & Particle physics
                High energy & Particle physics

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