Moonshine for Rudvalis's sporadic group II

Abstract

In Part I we introduced the notion of enhanced vertex operator superalgebra, and constructed an example which is self-dual, has rank 28, and whose full symmetry group is a seven-fold cover of the sporadic simple group of Rudvalis. In this article we construct a second enhanced vertex operator superalgebra whose full automorphism group is a cyclic cover of the Rudvalis group. This new example is self-dual and has rank -28. As in Part I, we can compute all the McKay--Thompson series associated to the action of the Rudvalis group explicitly. We observe that these series, when considered together with those of Part I, satisfy a genus zero property.