We provide a physics derivation of Monstrous moonshine. We show that the
McKay-Thompson series Tg, 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 mg, constructed by Borcherds and Carnahan. We argue that
mg 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.Comment: 73 pages, with results summarized in introduction. v2: added a
discussion about coupling to gravity (section 3.3), additional references,
minor corrections and improvement