Note on twisted elliptic genus of K3 surface

By Tohru Eguchi, Kazuhiro Hikami. 2010

164 citations recorded by the source corpus.

Abstract We discuss the possibility of Mathieu group M 24 acting as symmetry group on the K3 elliptic genus as proposed recently by Ooguri, Tachikawa and one of the present authors. One way of testing this proposal is to derive the twisted elliptic genera for all conjugacy classes of M 24 so that we can determine the unique decomposition of expansion coefficients of K3 elliptic genus into irreducible representations of M 24 . In this Letter we obtain all the hitherto unknown twisted elliptic genera and find a strong evidence of Mathieu moonshine.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8fb529f861157142e7e06d59574fb41384a79712

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In Algebra and Number Theory

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Citations in the corpus

Mathieu Moonshine in the elliptic genus of K3 (2010, methodology): “(2)After posting the first version of this paper on the arXiv, we were informed by Tohru Eguchi that they have independently obtained explicit formulae for these twining genera which agree with ours, see [24].”
Symmetries of K3 sigma models (2011, background): “Using these modular properties as well as the explicit knowledge of the first few coefficients that follow from the observation of [1], all twining genera could be determined [3, 4, 5, 6].”
Umbral Moonshine (2012, background): “In fact we can expect thismoonshine structure to encompass more groups beyond the monster and M24: In this paper we identify the M24 observation as one of a family of correspondences between finite groups and (vector-valued) mock modular forms, with each member in the family admitting a natural anal”