Vol. 3, No. 2, 2021

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Supersymmetry and the Suzuki chain

Theo Johnson-Freyd

Vol. 3 (2021), No. 2, 309–359
Abstract

We classify N=1 SVOAs with no free fermions and with bosonic subalgebra a simply connected WZW algebra which is not of type E. The latter restriction makes the classification tractable; the former restriction implies that the N=1 automorphism groups of the resulting SVOAs are finite. We discover two infinite families and nine exceptional examples. The exceptions are all related to the Leech lattice: their automorphism groups are the larger groups in the Suzuki chain ( Co1, Suz:2, G2(4):2, J2:2, U3(3):2) and certain large centralizers therein (210:M12:2, M12:2, U4(3):D8, M21:22). Along the way, we elucidate fermionic versions of a number of VOA operations, including simple current extensions, orbifolds, and ’t Hooft anomalies.

Keywords
finite groups, sporadic groups, vertex operator algebras, supersymmetry, conformal field theory
Mathematical Subject Classification 2010
Primary: 17B69, 20D08, 81Q60
Milestones
Received: 9 September 2019
Revised: 3 February 2020
Accepted: 18 February 2020
Published: 5 December 2020
Authors
Theo Johnson-Freyd
Perimeter Institute for Theoretical Physics
Waterloo ON
Canada