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A Borcherds–Kac–Moody Superalgebra with Conway Symmetry

Harrison, Sarah M. and Paquette, Natalie M. and Volpato, Roberto (2019) A Borcherds–Kac–Moody Superalgebra with Conway Symmetry. Communications in Mathematical Physics, 370 (2). pp. 539-590. ISSN 0010-3616. doi:10.1007/s00220-019-03518-0.

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We construct a Borcherds–Kac–Moody (BKM) superalgebra on which the Conway group Co0Co0acts faithfully. We show that the BKM algebra is generated by the physical states (BRST cohomology classes) in a chiral superstring theory. We use this construction to produce denominator identities for the chiral partition functions of the Conway module Vs♮, a supersymmetric c=12 chiral conformal field theory whose (twisted) partition functions enjoy moonshine properties and which has automorphism group isomorphic to Co0. In particular, these functions satisfy a genus zero property analogous to that of monstrous moonshine. Finally, we suggest how one may promote the denominators to spacetime BPS indices in type II string theory, which might thus furnish a physical explanation of the genus zero property of Conway moonshine.

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Paquette, Natalie M.0000-0003-2078-7165
Additional Information:© 2019 Springer-Verlag GmbH Germany, part of Springer Nature. Received: 22 May 2018; Accepted: 11 June 2019; First Online: 23 July 2019. We thank S. Carnahan, J. Duncan, D. Persson, N. Scheithauer and T. Wrase for useful comments and discussions. We are especially grateful to J. Duncan for helpful comments on an earlier version of the draft. S.H. is supported by the National Science and Engineering Council of Canada and the Canada Research Chairs program. N.P. is supported by a Sherman Fairchild Postdoctoral Fellowship. R.V. is supported by a grant from ‘Programma per giovani ricercatori Rita Levi Montalcini’. The authors acknowledge support from the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611. N.P. gratefully acknowledges the Perimeter Institute of Theoretical Physics for hospitality and support during the final stages of this work. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Canada Research Chairs ProgramUNSPECIFIED
Sherman Fairchild FoundationUNSPECIFIED
Programma per giovani ricercatori Rita Levi MontalciniUNSPECIFIED
Department of Energy (DOE)DE-SC0011632
Issue or Number:2
Record Number:CaltechAUTHORS:20190723-105653746
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Official Citation:Harrison, S.M., Paquette, N.M. & Volpato, R. Commun. Math. Phys. (2019) 370: 539.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:97355
Deposited By: Tony Diaz
Deposited On:23 Jul 2019 20:23
Last Modified:16 Nov 2021 17:31

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