Mathieu Moonshine and N=2 String Compactifications

TL;DR

This paper explores the extension of Mathieu moonshine to string dualities, linking sporadic group representations to physical indices and geometric invariants in heterotic and type IIA string compactifications.

Contribution

It provides evidence that Mathieu moonshine phenomena extend to dual string theories and connects group representations to geometric and physical quantities in these models.

Findings

M_{24} representations govern the supersymmetric index

M_{24} appears in Gromov--Witten invariants

Extension of Mathieu moonshine to string dualities

Abstract

There is a `Mathieu moonshine' relating the elliptic genus of K3 to the sporadic group M_{24}. Here, we give evidence that this moonshine extends to part of the web of dualities connecting heterotic strings compactified on K3 \times T^2 to type IIA strings compactified on Calabi-Yau threefolds. We demonstrate that dimensions of M_{24} representations govern the new supersymmetric index of the heterotic compactifications, and appear in the Gromov--Witten invariants of the dual Calabi-Yau threefolds, which are elliptic fibrations over the Hirzebruch surfaces F_n.