Vertex superalgebras over fields of prime characteristic

Abstract

This paper is to study vertex superalgebras over a field of prime characteristic. For a general 12Z-graded vertex superalgebra V, Zhu's A(V) theory is examined with some suitable modifications. Among the main results, Zhu's algebras of certain affine vertex superalgebras and Neveu-Schwarz vertex superalgebras, and irreducible modules for certain quotient vertex superalgebras associated to p-center, are determined. Irreducible modules for Clifford vertex superalgebras are also determined and a complete reducibility theorem is obtained.