Landau-Ginzburg Orbifolds and Symmetries of K3 CFTs

TL;DR

This paper investigates the connection between moonshine phenomena and K3 string theory by computing twined elliptic genera in Landau-Ginzburg models, revealing new links between symmetries and moonshine predictions.

Contribution

It provides the first explicit computation of twining functions in LG models matching various moonshine cases, strengthening the link between K3 symmetries and moonshine.

Findings

Twining functions from Mathieu, umbral, and Conway moonshine are realized in LG models.

All functions from $M_{11} imes 2.M_{12}$ moonshine appear as explicit twining genera.

Results support the relevance of umbral moonshine in K3 symmetry analysis.

Abstract

Recent developments in the study of the moonshine phenomenon, including umbral and Conway moonshine, suggest that it may play an important role in encoding the action of finite symmetry groups on the BPS spectrum of K3 string theory. To test and clarify these proposed K3-moonshine connections, we study Landau-Ginzburg orbifolds that flow to conformal field theories in the moduli space of K3 sigma models. We compute K3 elliptic genera twined by discrete symmetries that are manifest in the UV description, though often inaccessible in the IR. We obtain various twining functions coinciding with moonshine predictions that have not been observed in physical theories before. These include twining functions arising from Mathieu moonshine, other cases of umbral moonshine, and Conway moonshine. For instance, all functions arising from $M_{11} \subset 2.M_{12}$ moonshine appear as explicit twining genera in the LG models, which moreover admit a uniform description in terms of its natural 12-dimensional representation. Our results provide strong evidence for the relevance of umbral moonshine for K3 symmetries, as well as new hints for its eventual explanation.