Monstrous BPS-algebras and the superstring origin of moonshine

Magazine article, 2016

We provide a physics derivation of Monstrous moonshine. We show that the McKay-Thompson series T-g, g epsilon 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 m(g), constructed by Borcherds and Carnahan. We argue that 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 mg an interpretation as a kind of BPS-algebra.