#### Vol. 3, No. 2, 2021

 Recent Issues Volume 3, Issue 2 Volume 3, Issue 1 Volume 2, Issue 4 Volume 2, Issue 3 Volume 2, Issue 2 Volume 2, Issue 1 Volume 1, Issue 4 Volume 1, Issue 3 Volume 1, Issue 2 Volume 1, Issue 1
 The Journal About the Journal Editorial Board Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN (electronic): 2576-7666 ISSN (print): 2576-7658 Author Index To Appear Other MSP Journals
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 (${Co}_{1}$, $Suz:2$, ${G}_{2}\left(4\right):2$, ${J}_{2}:2$, ${U}_{3}\left(3\right):2$) and certain large centralizers therein (${2}^{10}:{M}_{12}:2$, ${M}_{12}:2$, ${U}_{4}\left(3\right):{D}_{8}$, ${M}_{21}:{2}^{2}$). 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