Monstrous BPS-algebras and the superstring origin of moonshine

We provide a physics derivation of Monstrous moonshine.We show that the McKay-Thompson series T g , g ∈ 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 m g an interpretation as a kind of BPSalgebra.