Possible Supersymmetric Kinematics

TL;DR

This paper explores supersymmetric extensions of various kinematical algebras derived from ext{AdS} algebra contractions, identifying which algebras admit supersymmetry and how they are interconnected.

Contribution

It classifies supersymmetric extensions of 22 kinematical algebras obtained via contraction methods, highlighting new supersymmetric realizations and their relationships.

Findings

Several algebras have supersymmetric extensions, including rak{p}_2, rak{h}_-, rak{p}', rak{c}_2, rak{g}'

Some algebras, like rak{n}_{-2} and rak{g}_2, lack supersymmetric extensions

Connections among superalgebras are explicitly established.

Abstract

The contraction method in different limits to obtain 22 different realizations of kinematical algebras is applied to study the supersymmetric extension of \AdS\ algebra and its contractions. It is shown that $\frak{p}_2$ $\frak{h}_-$, $\frak{p}'$, $\frak{c}_2$ and $\frak{g}'$ algebras, in addition to $\frak{d}_-$, $\frak{p}$, $\frak{n}_-$, $\frak{g}$ and $\frak{c}$ algebras, have supersymmetric extension, while $\frak{n}_{-2}$, $\frak{g}_2$ and $\frak{g}'_2$ algebras have no supersymmetric extension. The connections among the superalgebras are established.