Mathieu twining characters for K3

TL;DR

This paper investigates the Mathieu group action on the elliptic genus of K3, showing that the associated twining characters have modular properties and satisfy replication identities, supporting the Mathieu moonshine conjecture.

Contribution

It provides evidence that the elliptic genus of K3 exhibits an M24 symmetry through analysis of twining characters and their modular properties.

Findings

Twining characters have good modular properties.

Twining characters satisfy replication identities.

Supports the conjecture of Mathieu group action on K3 elliptic genus.

Abstract

The analogue of the McKay-Thompson series for the proposed Mathieu group action on the elliptic genus of K3 is analysed. The corresponding NS-sector twining characters have good modular properties and satisfy remarkable replication identities. These observations provide strong support for the conjecture that the elliptic genus of K3 carries indeed an action of the Mathieu group M24.