Spinor Algebras

TL;DR

This paper explores supersymmetry algebras in various space-time signatures, clarifying their structure, classification, and relation to conformal algebras, with a focus on spinor and orthosymplectic algebra frameworks.

Contribution

It provides a comprehensive classification of minimal and maximal super conformal algebras across arbitrary signatures and their connection to spin groups and orthosymplectic algebras.

Findings

Classification of minimal super conformal algebras linked to Spin(s,t) groups.

Identification of maximal super conformal algebras via orthosymplectic algebras.

Elucidation of the relation between super Poincaré and super conformal algebras.

Abstract

We consider supersymmetry algebras in space-times with arbitrary signature and minimal number of spinor generators. The interrelation between super Poincar\'e and super conformal algebras is elucidated. Minimal super conformal algebras are seen to have as bosonic part a classical semimisimple algebra naturally associated to the spin group. This algebra, the Spin$(s,t)$-algebra, depends both on the dimension and on the signature of space time. We also consider maximal super conformal algebras, which are classified by the orthosymplectic algebras.