Mathieu Moonshine and the Geometry of K3 Surfaces

2013/09/10 by Creutzig, Thomas, Hoehn, Gerald
#FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Number Theory (math.NT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1309.2671

Abstract

We compare the moonshine observation of Eguchi, Ooguri and Tachikawa relating the Mathieu group M₂4 and the complex elliptic genus of a K3 surface with the symmetries of geometric structures on K3 surfaces. Two main results are that the complex elliptic genus of a K3 surface is a virtual module for the Mathieu group M₂4 and also for a certain vertex operator superalgebra V^G where G is the holonomy group.

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