Unravelling Mathieu Moonshine

Abstract

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, Phi_{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.

20 pages; v2: New subsection on non-symplectic cases added v3: Some typos (a couple of sign errors) fixed

References in corpus (13)

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Cited by in corpus (19)

• BKM Lie superalgebras from counting twisted CHL dyons
• Fricke S-duality in CHL models
• Mock Modular Mathieu Moonshine Modules
• The Largest Mathieu Group and (Mock) Automorphic Forms
• Generalised Mathieu Moonshine
• BKM Lie superalgebras from counting twisted CHL dyons -- II
• Twining Genera of (0,4) Supersymmetric Sigma Models on K3
• BPS Saturated String Amplitudes: K3 Elliptic Genus and Igusa Cusp Form
• Dualities in CHL-Models
• Eta Products, BPS States and K3 Surfaces
• Umbral Moonshine and K3 Surfaces
• Mathieu Moonshine and Orbifold K3s
• Second Quantized Mathieu Moonshine
• Refined Partition Functions for Open Superstrings with 4, 8 and 16 Supercharges
• Positivity of discrete information for CHL black holes
• Two moonshines for $L_2(11)$ but none for $M_{12}$
• Mathieu Moonshine and Siegel Modular Forms
• $\widehat{sl(2)}$ decomposition of denominator formulae of some BKM Lie superalgebras
• $\widehat{sl(2)}$ decomposition of denominator formulae of some BKM Lie superalgebras -- II