Landau-Ginzburg orbifolds and symmetries of K 3 CFTs
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 K 3 string theory. To test and clarify these proposed K 3 -moonshine connections, we study Landau-Ginzburg orbifolds that flow to conformal field theories in the moduli space of K 3 sigma models. We compute K 3 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 c 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. Finally, our results provide strong evidence for the relevance of umbral moonshine for K 3 symmetries, as well as new hints for its eventual explanation.