Mathieu Moonshine and symmetries of K3 σ-models

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 σ-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.