Vertex operator superalgebras and the 16-fold way.

Let V be a vertex operator superalgebra with the natural order 2 automorphism σ. Under suitable conditions on V, the σ-fixed subspace V0 is a vertex operator algebra and the V0-module category CV0 is a modular tensor category. In this paper, we prove that CV0 is a fermionic modular tensor category and the Müger centralizer CV00 of the fermion in CV0 is generated by the irreducible V0-submodules of the V-modules. In particular, CV00 is a super-modular tensor category and CV0 is a minimal modular extension of CV00. We provide a construction of a vertex operator superalgebra Vl for each positive integer l such that C(Vl)0 is a minimal modular extension of CV00. We prove that these modular tensor categories C(Vl)0 are uniquely determined, up to equivalence, by the congruence class of l modulo 16. [ABSTRACT FROM AUTHOR]