Duncan--Frenkel twisted chiral gravity conjecture

Let $\Gamma_g$ be the group associated to $g\in\mathbb{M}$, and let $T^{(-1)}_{\Gamma_g}$ denote the normalized Rademacher sum attached to $\Gamma_g$. Duncan--Frenkel conjecture. There exists a monster-indexed family of twisted chiral three-dimensional gravity theories whose genus-one partition functions at

$$\mu=\sqrt{-\Lambda}=1/16G$$

are given by $T^{(-1)}_{\Gamma_g}(-1/\tau)$. The conjecture seeks a physical realization of the principal-modulus properties of monstrous moonshine through a family of twisted gravity theories; the specific non-trivial modular fact about these functions is proven by Carnahan, but the existence of the physical theories is not thereby established.