Mathieu twining characters for K3

By M. Gaberdiel, S. Hohenegger, R. Volpato. 2010

158 citations recorded by the source corpus.

The analogue of the McKay-Thompson series for the proposed Mathieu group action on the elliptic genus of K3 is analysed. The corresponding NS-sector twining characters have good modular properties and satisfy remarkable replication identities. These observations provide strong support for the conjecture that the elliptic genus of K3 carries indeed an action of the Mathieu group $ {\mathbb{M}_{24}} $.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7557850134ed74283ed5c9c478a8b9e3ef5be5f0

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Citations in the corpus

Umbral Moonshine (2012, background): “This idea has been implemented successfully in [19, 20, 21, 22] and provides strong”
K3 Surfaces, N=4 Dyons, and the Mathieu Group M24 (2010, background): “For the two examples (g = 2B, 4A) of elements that are in M24 but not in M23, slightly more subtle modular properties of the corresponding twisted elliptic genus Zg(τ, z) are discussed in [64]6.”
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].”
Mathieu Moonshine in the elliptic genus of K3 (2010, methodology): “In order to test this idea it is then again natural to consider the ‘twining genera’ φg(τ, z), where one replaces dim(Hn) by the corresponding character TrHn(g), with g ∈ M24 [7, 8].”
Note on twisted elliptic genus of K3 surface (2010, methodology): “Twisted elliptic genera of the type I has been obtained previously [2, 5, 13].”
Notes on the K3 Surface and the Mathieu Group M 24 (2010, result): “…· · , (1–6) could be naturally decomposed into the sum of the dimension of the irreducible representation of the monster 1 The tentative decomposition of A7 shown in a previous version of this paper was incorrect in view of a later study of twisted elliptic genus in [Cheng 10, Gaberdiel et al. 10].”