Nonassociative superconformal algebras

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 s...

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Bibliographic Details
Published in:Journal of mathematical physics 1991-09, Vol.32 (9), p.2285-2297
Main Authors: Hasiewicz, Z., Defever, F., Troost, W.
Format: Article
Language:English
Subjects:
Algebra
Exact sciences and technology
Mathematics
Nonassociative rings and algebras
Sciences and techniques of general use
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Summary: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 S 7 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.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.529151