A linear realization for the new space-time superalgebras in ten and eleven dimensions

TL;DR

This paper demonstrates a linear realization of new superalgebra extensions in ten and eleven dimensions, showing equivalence of nonlinear and linear group representations and providing a coset space parametrization.

Contribution

It introduces a linear realization for recently discovered superalgebra extensions in high-dimensional theories, clarifying their structure and representations.

Findings

Linear realization of superalgebra extensions established.

Equivalence of nonlinear and linear group representations shown.

Coset space parametrization for linear transformations provided.

Abstract

The new extensions of the Poincar\'e superalgebra recently found in ten and eleven dimensions are shown to admit a linear realization. The generators of the nonlinear and linear group transformations are shown to fall into equivalent representations of the superalgebra. The parametrization of the coset space $G/H$, with $G$ a given extended supergroup and $H$ the Lorentz subgroup, that corresponds to the linear transformations is presented.