The Art of Orbifolding by Huge Non-Abelian Groups

Abstract

We compute torus partition functions of orbifolds of two-dimensional chiral fermions by huge non-Abelian groups involving the Conway group, one of the sporadic finite simple groups. This seemingly standard problem turns out to contain, somewhat unexpectedly, multiple major issues hitherto unresolved, both at the level of the principle and at the level of practice. We describe in detail how they can be overcome. Although the methods described in this paper are generally applicable, the choice of the particular orbifolds we consider in this paper was motivated by the search for the periodicity element of topological modular forms. We will provide a brief introduction to this question, to explain why all the techniques in this paper had to be developed. Unfortunately, the orbifolds we considered turned out not to be the periodicity element.