Brane Content of Branes' States

TL;DR

This paper investigates the decomposition of unitary irreducible representations of tensorial Poincaré algebras, analyzing particle content and little groups for branes and preon states across various dimensions, revealing new structural insights.

Contribution

It provides a detailed calculation of little groups and particle spectra for tensorial Poincaré algebras, including novel classifications of preons and branes in different dimensions.

Findings

Results align with Vasiliev's in 4D generalized space-time.

Translational little groups of massless particles relate to pure brane algebras.

Distinct preon types identified in 11D due to spinor properties.

Abstract

The problem of decomposition of unitary irreps of (super) tensorial (i.e. extended with tensorial charges) Poincar{\'e} algebra w.r.t. its different subalgebras is considered. This requires calculation of little groups for different configurations of tensor charges. Particularly, for preon states (i.e. states with maximal supersymmetry) in different dimensions the particle content is calculated, i.e. the spectrum of usual Poincar{\'e} representations in the preon representation of tensorial Poincar{\'e}. At d=4 results coincide with (and may provide another point of view on) the Vasiliev's results in field theories in generalized space-time. The translational subgroup of little groups of massless particles and branes is shown to be (and coincide with, at d=4) a subgroup of little groups of "pure branes" algebras, i.e. tensorial Poincar{\'e} algebras without vector generators. At 11d it is shown that, contrary to lower dimensions, spinors are not homogeneous space of Lorentz group, and one have to distinguish at least 7 different kinds of preons.