Generalised Mathieu Moonshine

TL;DR

This paper constructs Mathieu twisted twining genera for K3's elliptic genus, demonstrating their modular properties and suggesting a possible underlying holomorphic VOA structure for Mathieu Moonshine.

Contribution

It introduces Mathieu twisted twining genera for K3, showing their modular behavior governed by a 3-cocycle, indicating a new structure in Mathieu Moonshine.

Findings

Twisted twining genera satisfy expected consistency conditions

Modular transformations controlled by a 3-cocycle in H^3(M_24,U(1))

Evidence for an underlying holomorphic VOA in 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.