Supersymmetry and the Suzuki chain

TL;DR

This paper classifies certain $N=1$ super vertex operator algebras with specific algebraic restrictions, discovering new families and exceptional cases related to the Leech lattice and Suzuki chain automorphism groups.

Contribution

It provides a classification of $N=1$ SVOAs with no free fermions and bosonic subalgebra as a non-$E$-type simply connected WZW algebra, revealing new families and exceptional examples.

Findings

Identified two infinite families of $N=1$ SVOAs.

Discovered nine exceptional examples related to the Leech lattice.

Connected automorphism groups to the Suzuki chain and large centralizers.

Abstract

We classify $N{=}1$ SVOAs with no free fermions and with bosonic subalgebra a simply connected WZW algebra which is not of type $\mathrm{E}$. 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 ($\mathrm{Co}_1$, $\mathrm{Suz}{:}2$, $\mathrm{G}_2(4){:}2$, $\mathrm{J}_2{:}2$, $\mathrm{U}_3(3){:}2$) and certain large centralizers therein ($2^{10}{:}\mathrm{M}_{12}{:}2$, $\mathrm{M}_{12}{:}2$, $\mathrm{U}_4(3){:}D_8$, $\mathrm{M}_{21}{:}2^2$). Along the way, we elucidate fermionic versions of a number of VOA operations, including simple current extensions, orbifolds, and 't Hooft anomalies.