Considerations on Super Poincare Algebras and their Extensions to Simple Superalgebras

TL;DR

This paper explores simple superalgebras extending super Poincaré algebras, analyzing their structure, contractions, and physical implications in various dimensions, especially 10 and 4.

Contribution

It classifies simple superalgebras extending super Poincaré algebras with up to 64 odd generators, including their contractions and physical relevance.

Findings

Some superalgebras can be interpreted as de Sitter or anti de Sitter superalgebras.

The number of odd generators varies due to spinor representation splitting.

Detailed analysis provided for dimensions 10 and 4.

Abstract

We consider simple superalgebras which are a supersymmetric extension of $\fspin(s,t)$ in the cases where the number of odd generators does not exceed 64. All of them contain a super Poincar\'e algebra as a contraction and another as a subalgebra. Because of the contraction property, some of these algebras can be interpreted as de Sitter or anti de Sitter superalgebras. However, the number of odd generators present in the contraction is not always minimal due to the different splitting properties of the spinor representations under a subalgebra. We consider the general case, with arbitrary dimension and signature, and examine in detail particular examples with physical implications in dimensions $d=10$ and $d=4$.