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Abstract
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We classify
SVOAs with no free fermions and with bosonic subalgebra a simply connected WZW algebra which
is not of type
.
The latter restriction makes the classification tractable; the former restriction implies
that the
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
(,
,
,
,
) and certain large
centralizers therein (,
,
,
).
Along the way, we elucidate fermionic versions of a number of VOA operations,
including simple current extensions, orbifolds, and ’t Hooft anomalies.
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Keywords
finite groups, sporadic groups, vertex operator algebras,
supersymmetry, conformal field theory
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Mathematical Subject Classification 2010
Primary: 17B69, 20D08, 81Q60
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Milestones
Received: 9 September 2019
Revised: 3 February 2020
Accepted: 18 February 2020
Published: 5 December 2020
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