Imaginary reflections and discrete symmetries in the heterotic Monster

Abstract

Let $\mathbb{M}$ be the Monster finite simple group. We give an interpretation of certain discrete symmetries of a family of heterotic string compactifications to $1+1$ dimensions in terms of discrete symmetries of the Monster Lie algebra $\mathfrak{m}$, and more generally Carnahan's family of Monstrous Lie algebras ${\mathfrak{m}}_g$, for $g\in \mathbb{M}$ of Fricke type. We relate a Weyl group-type reflection $w_{\im}$, with respect to an imaginary simple root, to a composition of T-duality, time reversal, and parity reversal transformations in the compactified heterotic string. The transformation $w_{\im}$ also has a natural permutation action on the BPS states of the compactified heterotic string.