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BPS algebras, genus zero and the heterotic Monster

Journal article
Authors Natalie M. Paquette
Daniel Persson
Roberto Volpato
Published in Journal of Physics A: Mathematical and Theoretical
Volume 50
ISSN 1751-8113
Publication year 2017
Published at Department of Mathematical Sciences
Language en
Links https://doi.org/10.1088/1751-8121/a...
Keywords BPS states, conformal feld theory, generalized kac-moody, heterotic string, Monstrous moonshine, string theory
Subject categories Mathematical Analysis

Abstract

© 2017 IOP Publishing Ltd. 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 - 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.

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