An Application of Collapsing Levels to the Representation Theory of Affine Vertex Algebras

We discover a large class of simple affine vertex algebras V-k(g), associated to basic Lie superalgebras g at non-admissible collapsing levels k, having exactly one irreducible g-locally finite module in the category O. In the case when g is a Lie algebra, we prove a complete reducibility result for V-k(g)-modules at an arbitrary collapsing level. We also determine the generators of the maximal ideal in the universal affine vertex algebra V-k(g) at certain negative integer levels. Considering some conformal embeddings in the simple affine vertex algebras V-1/2(C-n) and V-4(E-7), we surprisingly obtain the realization of non-simple affine vertex algebras of types B and D having exactly one nontrivial ideal.