Imaginary reflections and discrete symmetries in the heterotic Monster

TL;DR

This paper explores the connection between discrete symmetries in heterotic string compactifications and the Monster Lie algebra, revealing how certain transformations relate to string dualities and BPS state permutations.

Contribution

It provides a novel interpretation of discrete symmetries in heterotic strings in terms of the Monster Lie algebra and its automorphisms, linking string dualities to algebraic structures.

Findings

Weyl group-type reflections correspond to T-duality, time reversal, and parity reversal.

The reflection $w_{\im}$ permutes BPS states in the heterotic string.

Discrete symmetries of string compactifications relate to automorphisms of the Monster Lie algebra.

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 $\frak m$, and more generally Carnahan's family of Monstrous Lie algebras $\frak m_g$, 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.