Super-de Sitter and alternative super-Poincar\'e symmetries

TL;DR

This paper introduces a novel superextension of the de Sitter algebra using a -grading, leading to an alternative super-Poincare9 algebra via contraction, expanding the understanding of supersymmetries in curved spacetime.

Contribution

It demonstrates that -graded superextensions exist for the de Sitter algebra and derives an alternative super-Poincare9 algebra through contraction methods.

Findings

De Sitter algebra -graded superextension constructed.

An alternative super-Poincare9 algebra obtained via contraction.

Contrasts with the anti-de Sitter case, which lacks a standard superextension.

Abstract

It is well-known that de Sitter Lie algebra $\mathfrak{o}(1,4)$ contrary to anti-de Sitter one $\mathfrak{o}(2,3)$ does not have a standard $\mathbb{Z}_2$-graded superextension. We show here that the Lie algebra $\mathfrak{o}(1,4)$ has a superextension based on the $\mathbb{Z}_2\times\mathbb{Z}_2$-grading. Using the standard contraction procedure for this superextension we obtain an {\it alternative} super-Poincar\'e algebra with the $\mathbb{Z}_2\times\mathbb{Z}_2$-grading.