Supersymmetry and the Suzuki chain

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.

arXiv comment35 pages. v4 corrects an error that caused one entry to be missing from the main theorem

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Cited by in corpus (4)

• Bosonic Rational Conformal Field Theories in Small Genera, Chiral Fermionization, and Symmetry/Subalgebra Duality
• Fermionic CFTs from topological boundaries in abelian Chern-Simons theories
• From vertex operator superalgebras to graded-local conformal nets and back
• Emergent Supersymmetry on the Edges