Spinor Algebras and Extended Superconformal Algebras

TL;DR

This paper explores the structure of supersymmetry algebras across various spacetime dimensions and signatures, highlighting how spinor properties uniquely determine their extensions.

Contribution

It provides a comprehensive classification of minimal and maximal superalgebras based on spinor representations in different dimensions and signatures.

Findings

Supersymmetry extensions are uniquely determined by spinor properties.

Classification of superalgebras for arbitrary spacetime dimensions.

Dependence of algebra properties on dimension mod 8 and signature mod 8.

Abstract

We consider supersymmetry algebras in arbitrary spacetime dimension and signature. Minimal and maximal superalgebras are given for single and extended supersymmetry. It is seen that the supersymmetric extensions are uniquely determined by the properties of the spinor representation, which depend on the dimension $D$ mod 8 and the signature $|\rho|$ mod 8 of spacetime.