Mathieu Moonshine and symmetries of K3 sigma models

TL;DR

This paper reviews the proposed connection between the Mathieu group M24 and K3 surface symmetries, discussing evidence and open questions about a potential non-linear sigma-model with M24 symmetry.

Contribution

It critically examines the EOT conjecture linking M24 to K3 elliptic genus and clarifies the discrepancy with known symmetry classifications.

Findings

No known K3 sigma-models have M24 as symmetry group

The EOT conjecture remains supported by indirect evidence

Open problems involve understanding the physical realization of M24 symmetry

Abstract

A recent observation by Eguchi, Ooguri and Tachikawa (EOT) suggests a relationship between the largest Mathieu group M24 and the elliptic genus of K3. This correspondence would be naturally explained by the existence of a non-linear sigma-model on K3 with the Mathieu group as its group of symmetries. However, all possible symmetry groups of K3 models have been recently classified and none of them contains M24. We review the evidence in favour of the EOT conjecture and discuss the open problems in its physical interpretation.