Nonassociative superconformal algebras

Abstract

A study of conventional superconformal not-necessarily Lie superalgebras is performed. A uniform prescription is given, leading to the definition of a family of structures with N=1,...,8 supersymmetries. For N≤4, Lie superalgebras are recovered, for N≥5 the algebras are nonassociative. The not-Lie superconformal algebras with N=5,6,7,8 share interesting common properties, relating them to the Cayley numbers, covariant derivation of spinors on the seven-sphere S7 and torsions on supercoset manifolds. The N=8 case is related to the (soft) constraint algebra of a recent reformulation of the Green’s–Schwarz superstring.