Constraints and Casimirs for Superpoincare and Supertranslation Algebras in various dimensions

TL;DR

This paper constructs covariant, supersymmetric constraints for massless and massive super Poincare algebras across various dimensions, clarifying their representations and the role of Casimirs and central charges.

Contribution

It introduces a universal covariant supersymmetric constraint for the super Poincare algebra applicable in any dimension, extending the concept of superspin Casimir to higher dimensions.

Findings

Unique representation fixing by the constraint for massless case

Generalization of superspin Casimir to arbitrary dimensions

Discussion of modifications due to scalar and tensorial central charges

Abstract

We describe, for arbitrary dimensions the construction of a covariant and supersymmetric constraint for the massless Super Poincare' algebra and we show that the constraint fixes uniquely the representation of the algebra. For the case of finite mass and in the absence of central charges we discuss a similar construction, which generalizes to arbitrary dimensions the concept of the superspin Casimir. Finally we discuss briefly the modifications introduced by central charges, both scalar and tensorial.