Mathieu Moonshine and Symmetry Surfing

TL;DR

This paper explores the Mathieu Moonshine phenomenon, proposing that symmetry surfing can be extended to all BPS states, providing a deeper understanding of the Mathieu group M24's role in K3 surface symmetries.

Contribution

It offers evidence that symmetry surfing can be generalized beyond lowest BPS states to all BPS states, advancing the conceptual understanding of Mathieu Moonshine.

Findings

Symmetry surfing can potentially be extended to all BPS states.

Evidence supports a broader role of Mathieu group M24 in K3 BPS spectra.

The approach links symmetries of different K3 models to Mathieu Moonshine.

Abstract

Mathieu Moonshine, the observation that the Fourier coefficients of the elliptic genus on K3 can be interpreted as dimensions of representations of the Mathieu group M24, has been proven abstractly, but a conceptual understanding in terms of a representation of the Mathieu group on the BPS states, is missing. Some time ago, Taormina and Wendland showed that such an action can be naturally defined on the lowest non-trivial BPS states, using the idea of `symmetry surfing', i.e., by combining the symmetries of different K3 sigma models. In this paper we find non-trivial evidence that this construction can be generalized to all BPS states.