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  Mathieu Moonshine and Orbifold K3s

Gaberdiel, M. R., & Volpato, R. (2014). Mathieu Moonshine and Orbifold K3s. In Conformal Field Theory, Automorphic Forms and Related Topics (Contributions in Mathematical and Computational Sciences; 8) (pp. 109-141). Springer.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-000F-A884-9 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-002B-A07E-E
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1206.5143 (Preprint), 331KB
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 Creators:
Gaberdiel, Matthias R., Author
Volpato, Roberto1, Author              
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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Free keywords: High Energy Physics - Theory, hep-th
 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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 Dates: 2012-06-2220132014
 Publication Status: Published in print
 Pages: 29 pages. Partially based on talk given by M.R.G. at the conference "Conformal Field Theory, Automorphic Forms and Related Topics", Heidelberg, 19-23 September 2011
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 Identifiers: arXiv: 1206.5143
URI: http://arxiv.org/abs/1206.5143
DOI: 10.1007/978-3-662-43831-2_5
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Title: Conformal Field Theory, Automorphic Forms and Related Topics
Place of Event: Heidelberg
Start-/End Date: 2011-09-19 - 2011-09-23

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Title: Conformal Field Theory, Automorphic Forms and Related Topics (Contributions in Mathematical and Computational Sciences; 8)
Source Genre: Proceedings
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Publ. Info: Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 109 - 141 Identifier: -