Algebraic structures on quasi-primary states in superconformal algebras

Abstract

Operator Product Expansions give algebraic structures on subspaces of quasi-primary vectors in superconformal algebras. The structures characterize the structures of superconformal algebras if they meet a criteria, while in some cases the spaces of quasi-primary vectors are finite dimensional. As an application the complete list of simple physical conformal superalgebras is given by classifying the corresponding algebraic structures on finite dimensional vector spaces. The list contains a one-parameter family of superconformal algebras with $4$ supercharges that is simple for general values.