Topological modularity of Monstrous Moonshine

TL;DR

This paper investigates the topological and modular properties of Monstrous Moonshine through orbifold constructions of the Monster conformal field theory, revealing divisibility properties related to McKay-Thompson series.

Contribution

It introduces new divisibility properties for orbifolds of the Monster CFT, connecting topological modular forms with generalized Moonshine and orbifold techniques.

Findings

Orbifolds by cyclic subgroups satisfy specific divisibility properties.

Orbifolds by non-abelian subgroups relate to Generalized Moonshine data.

Divisibility properties help rule out certain extremal holomorphic CFTs.

Abstract

We explore connections among Monstrous Moonshine, orbifolds, the Kitaev chain and topological modular forms. Symmetric orbifolds of the Monster CFT, together with further orbifolds by subgroups of Monster, are studied and found to satisfy the divisibility property, which was recently used to rule out extremal holomorphic conformal field theories. For orbifolds by cyclic subgroups of Monster, we arrive at divisibility properties involving the full McKay-Thompson series. Orbifolds by non-abelian subgroups of Monster are further considered by utilizing the data of Generalized Moonshine.