BPS algebras, genus zero and the heterotic Monster
Journal article, 2017

In this note, we expand on some technical issues raised in (Paquette et al 2016 Commun. Number Theory Phys. 10 433-526) by the authors, as well as providing a friendly introduction to and summary of our previous work. We construct a set of heterotic string compactifications to 0 + 1 dimensions intimately related to the Monstrous moonshine module of Frenkel, Lepowsky, and Meurman (and orbifolds thereof). Using this model, we review our physical interpretation of the genus zero property of Monstrous moonshine. Furthermore, we show that the space of (second-quantized) BPS-states forms a module over the Monstrous Lie algebras m(g)-some of the first and most prominent examples of Generalized Kac-Moody algebras-constructed by Borcherds and Carnahan. In particular, we clarify the structure of the module present in the second-quantized string theory. We also sketch a proof of our methods in the language of vertex operator algebras, for the interested mathematician.

monstrous moonshine

string theory

conformal field theory

heterotic string

BPS states

generalized kac-moody


N. M. Paquette

Stanford University

Daniel Persson

University of Gothenburg

Chalmers, Physics, Theoretical Physics

Chalmers, Mathematical Sciences, Algebra and geometry

R. Volpato

University of Padua

Journal of Physics A: Mathematical and Theoretical

1751-8113 (ISSN) 1751-8121 (eISSN)

Vol. 50 41

Subject Categories

Mathematical Analysis



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