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Unravelling Mathieu moonshine
Published in
Volume: 864
Issue: 3
Pages: 823 - 839
The D1-D5-KK-p system naturally provides an infinite-dimensional module graded by the dyonic charges whose dimensions are counted by the Igusa cusp form, Φ 10(Z). We show that the Mathieu group, M 24, acts on this module by recovering the Siegel modular forms that count twisted dyons as a trace over this module. This is done by recovering Borcherds product formulae for these modular forms using the M 24 action. This establishes the correspondence ('moonshine') proposed in arXiv:0907.1410 that relates conjugacy classes of M 24 to Siegel modular forms. This also, in a sense that we make precise, subsumes existing moonshines for M 24 that relates its conjugacy classes to eta-products and Jacobi forms. © 2012 Elsevier B.V.
About the journal
JournalNuclear Physics B
Open AccessNo