Communications in Number Theory and Physics

Volume 7 (2013)

Number 1

Generalized Mathieu Moonshine

Pages: 145 – 223



Matthias R. Gaberdiel (Institut für Theoretische Physik, ETH Zürich, Zürich, Switzerland)

Daniel Persson (Fundamental Physics, Chalmers University of Technology, Gothenburg, Sweden)

Henrik Ronellenfitsch (Max-Planck-Institut für Dynamik und Selbstorganisation (MPIDS), Göttingen, Germany)

Roberto Volpato (Max-Planck-Institut für Gravitationsphysik, Golm, Germany)


The Mathieu twisted twining genera, i.e., the analogues of Norton’s generalized 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.

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