The Moonshine Module for Conway's Group

Understand

We exhibit an action of Conway's group---the automorphism group of the Leech lattice---on a distinguished super vertex operator algebra, and we prove that the associated graded trace functions are normalized principal moduli, all having vanishing constant terms in their Fourier expansion.

• Thus we construct the natural analogue of the Frenkel--Lepowsky--Meurman moonshine module for Conway's group.
• The super vertex operator algebra we consider admits a natural characterization, in direct analogy with that conjectured to hold for the moonshine module vertex operator algebra.
• It also admits a unique canonically-twisted module, and the action of the Conway group naturally extends.