Holomorphic integer graded vertex superalgebras

Abstract

In this paper, we study holomorphic [Formula: see text]-graded vertex superalgebras. We prove that all such vertex superalgebras of central charge [Formula: see text] and [Formula: see text] are purely even. For the case of central charge [Formula: see text] we prove that the weight-one Lie superalgebra is either zero, of superdimension [Formula: see text], or else is one of an explicit list of 1332 semisimple Lie superalgebras.