Monstrous BPSAlgebras and the Superstring Origin of Moonshine
Abstract
We provide a physics derivation of Monstrous moonshine. We show that the McKayThompson series $T_g$, $g\in \mathbb{M}$, can be interpreted as supersymmetric indices counting spacetime BPSstates in certain heterotic string models. The invariance groups of these series arise naturally as spacetime Tduality 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 BPSstates 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 BPSstates. This gives $\mathfrak{m}_g$ an interpretation as a kind of BPSalgebra.
 Publication:

arXiv eprints
 Pub Date:
 January 2016
 arXiv:
 arXiv:1601.05412
 Bibcode:
 2016arXiv160105412P
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Number Theory;
 Mathematics  Representation Theory
 EPrint:
 73 pages, with results summarized in introduction. v2: added a discussion about coupling to gravity (section 3.3), additional references, minor corrections and improvements