Note on Twisted Elliptic Genus of K3 Surface

TL;DR

This paper investigates the potential symmetry of the K3 elliptic genus under the Mathieu group M24, deriving twisted elliptic genera for all conjugacy classes to support the Mathieu moonshine conjecture.

Contribution

It derives all previously unknown twisted elliptic genera for M24 conjugacy classes, providing strong evidence for Mathieu moonshine.

Findings

Derived all twisted elliptic genera for M24 conjugacy classes.

Found strong evidence supporting Mathieu moonshine.

Enhanced understanding of K3 elliptic genus symmetries.

Abstract

We discuss the possibility of Mathieu group M24 acting as symmetry group on the K3 elliptic genus as proposed recently by Ooguri, Tachikawa and one of the present authors. One way of testing this proposal is to derive the twisted elliptic genera for all conjugacy classes of M24 so that we can determine the unique decomposition of expansion coefficients of K3 elliptic genus into irreducible representations of M24. In this paper we obtain all the hitherto unknown twisted elliptic genera and find a strong evidence of Mathieu moonshine.