Super-moonshine for Conway's largest sporadic group

Abstract

We study a self-dual $N=1$ super vertex operator algebra and prove that the full symmetry group is Conway's largest sporadic simple group. We verify a uniqueness result that is analogous to that conjectured to characterize the Moonshine vertex operator algebra (VOA). The action of the automorphism group is sufficiently transparent that one can derive explicit expressions for all the McKay-Thompson series. A corollary of the construction is that the perfect double cover of the Conway group may be characterized as a point-stabilizer in a spin module for the Spin group associated to a $24$-dimensional Euclidean space