3 N ov 2 00 8 Moonshine for Rudvalis ’ s sporadic group II ∗

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.