Monstrous BPS-Algebras and the Superstring Origin of Moonshine

TL;DR

This paper offers a physics-based explanation for Monstrous moonshine by linking McKay-Thompson series to BPS-states in heterotic string models, revealing new algebraic structures and duality symmetries.

Contribution

It introduces a novel interpretation of Monstrous moonshine through heterotic string theory, connecting BPS-states to Monstrous Lie algebras and spacetime dualities.

Findings

McKay-Thompson series as supersymmetric indices of BPS-states

Spacetime T-duality groups explain genus zero property

Monstrous Lie algebras as BPS-algebras from broken gauge symmetries

Abstract

We provide a physics derivation of Monstrous moonshine. We show that the McKay-Thompson series $T_g$, $g\in \mathbb{M}$, can be interpreted as supersymmetric indices counting spacetime BPS-states in certain heterotic string models. The invariance groups of these series arise naturally as spacetime T-duality groups and their genus zero property descends from the behaviour of these heterotic models in suitable decompactification limits. We also show that the space of BPS-states forms a module for the Monstrous Lie algebras $\mathfrak{m}_g$, constructed by Borcherds and Carnahan. We argue that $\mathfrak{m}_g$ arise in the heterotic models as algebras of spontaneously broken gauge symmetries, whose generators are in exact correspondence with BPS-states. This gives $\mathfrak{m}_g$ an interpretation as a kind of BPS-algebra.