BPS algebras, genus zero and the heterotic Monster. (8th September 2017)

• Record Type: Journal Article
• Authors: Paquette, Natalie M; Persson, Daniel; Volpato, Roberto
• Is Part Of: Journal of physics. Volume 50:Number 41(2017)
• Publication Date: 2017-09-08
• Subjects: monstrous moonshine -- generalized kac–moody -- heterotic string -- conformal field theory -- string theory -- BPS states; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa8443
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: 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.