Generalised Mathieu Moonshine

Abstract

The Mathieu twisted twining genera, i.e. the analogues of Norton's generalised Moonshine functions, are constructed for the elliptic genus of K3. It is shown that they satisfy the expected consistency conditions, and that their behaviour under modular transformations is controlled by a 3-cocycle in H^3(M_24,U(1)), just as for the case of holomorphic orbifolds. This suggests that a holomorphic VOA may be underlying Mathieu Moonshine.

71 pages; (v2) ancillary files correctly included; (v3) (final version), minor improvements, completed proof in sec. 3.3, tables added, references added

References in corpus (12)

• Notes on the K3 Surface and the Mathieu group M_24
• Quantum Black Holes, Wall Crossing, and Mock Modular Forms
• Note on Twisted Elliptic Genus of K3 Surface
• Chiral de Rham complex and the half-twisted sigma-model
• K3 Surfaces, N=4 Dyons, and the Mathieu Group M24
• Discrete Information from CHL Black Holes
• BKM Lie superalgebras from counting twisted CHL dyons
• Generalized Moonshine IV: Monstrous Lie algebras
• Brewing moonshine for Mathieu
• Second Quantized Mathieu Moonshine
• Mathieu Moonshine and Orbifold K3s
• The McKay-Thompson series of Mathieu Moonshine modulo two

Cited by in corpus (17)

• Holomorphic SCFTs with small index
• Mock Modular Mathieu Moonshine Modules
• Fricke S-duality in CHL models
• Umbral Moonshine and the Niemeier Lattices
• The Moonshine Anomaly
• BKM Lie superalgebras from counting twisted CHL dyons -- II
• Anomalies, Extensions and Orbifolds
• K3 String Theory, Lattices and Moonshine
• Exceptional Algebra and Sporadic Groups at c=12
• Generalised Umbral Moonshine
• Eta Products, BPS States and K3 Surfaces
• Second Quantized Mathieu Moonshine
• Umbral Moonshine and K3 Surfaces
• Third Homology of some Sporadic Finite Groups
• Horizon states and the sign of their index in $\mathcal{N}=4$ dyons
• Mathieu Moonshine and Siegel Modular Forms
• State counting on fibered CY-3 folds and the non-Abelian Weak Gravity Conjecture