Superconformal algebras and Clifford algebras

Abstract

It is shown that superconformal Lie superalgebras contain a Clifford algebra structure. This is used to present a classification of these algebras under the following assumptions: only fields with (half-)integer conformal dimension between 2 and 1/2 , and a nonzero central element. It turns out that the number of supersymmetry generators must be less than or equal to 4. More generally, the so(N) series, as well as some nonassociative algebras connected to S7, also have a natural place in this Clifford algebra framework.