Miranda Cheng

$M_{24}$, K3 String Theory, and Holographic Moonshine



Abstract

A theory of moonshine connects a sporadic group and a set of modular objects, and string theory has been proven crucial in the understanding of such an unexpected moonshine phenomenon. Recently, a conjectural relation has been proposed between the elliptic cohomology of K3 surfaces and the sporadic group Mathieu 24. This proposal has passed various non-trivial checks and points to a novel theory of $M_{24}$ moonshine. Moreover, via the BPS spectrum of type II string theory on $K3\times T^2$, it gets connected to another version of $M_{24}$-moonshine that has been previously proven. In this talk I will summarize the intricate web of objects with (conjectured) $M_{24}$-symmetry including cusp forms, weak Jacobi forms, Mock modular forms, automorphic forms, and a generalized Kac-Moody algebra, with the link between them provided by K3-compactified string theory.