We constructed an operator algebraic counterpart of the Moonshine vertex operator algebra with Longo before. Its automorphism group is the Monster group and its character is the modular elliptic j-function without the constant term. We have now constructed its "super" analogue for Conway's sporadic group Co1, following work of Duncan for an enhanced super vertex operator algebra.
The notion of a spectral triple gives a "noncommutative manifold" in the framework of noncommutative geometry of Connes. With Carpi, Hillier and Longo, we have constructed a net of spectral triples from a certain representation of the super Virasoro algebra. This gives a bridge between superconformal field theory and noncommutative geometry.