PIRSA:18030124

Video URL

https://pirsa.org/18030124

Borcherds-Kac-Moody Algebras, Moonshine VOAs, and String Theory

Paquette, N. (2018). Borcherds-Kac-Moody Algebras, Moonshine VOAs, and String Theory. Perimeter Institute for Theoretical Physics. https://pirsa.org/18030124

Paquette, Natalie. Borcherds-Kac-Moody Algebras, Moonshine VOAs, and String Theory. Perimeter Institute for Theoretical Physics, Mar. 26, 2018, https://pirsa.org/18030124 

          @misc{ scivideos_PIRSA:18030124,
            doi = {10.48660/18030124},
            url = {https://pirsa.org/18030124},
            author = {Paquette, Natalie},
            keywords = {Mathematical physics},
            language = {en},
            title = {Borcherds-Kac-Moody Algebras, Moonshine VOAs, and String Theory},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2018},
            month = {mar},
            note = {PIRSA:18030124 see, \url{https://scivideos.org/index.php/pirsa/18030124}}
          }

Natalie Paquette University of Washington

Talk numberPIRSA:18030124
DOI10.48660/18030124
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

In this talk we will review our physical proposal, with D. Persson and R. Volpato, to understand the genus zero property of monstrous moonshine. The latter was proven by Borcherds in 1992 by brute-force computation but has since resisted a conceptual understanding. We embed the Monster VOA of Frenkel-Lepowsky-Meurman into a heterotic string compactification and use physical arguments, i.e. T-dualities and decompactification limits, to understand the genus zero property. We find that the Monster Lie algebra (a Generalized, or Borcherds-Kac-Moody algebra) acts as a sort of "algebra of BPS states". We also sketch an analogous proposal, with S. Harrison and R. Volpato, for Conway moonshine using the type II string. Along the way we construct a new super Borcherds-Kac-Moody algebra on which the Conway group acts faithfully and prove its (twisted) denominator identities, which should be identified with BPS state counts in our string theory.