Supersymmetry and the Suzuki chain

摘要

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(4):2, J_2:2, U_3(3):2) and certain large centralizers therein (2~(10):M_(12):2, M_(12):2, U_4(3):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.