The massless irreducible representation in E theory and how bosons can appear as spinors

Abstract

We study in detail the irreducible representation of [Formula: see text] theory that corresponds to massless particles. This has little algebra [Formula: see text] and contains 128 physical states that belong to the spinor representation of [Formula: see text]. These are the degrees of freedom of maximal supergravity in eleven dimensions. This smaller number of the degrees of freedom, compared to what might be expected, is due to an infinite number of duality relations which in turn can be traced to the existence of a subaglebra of [Formula: see text] which forms an ideal and annihilates the representation. We explain how these features are inherited into the covariant theory. We also comment on the remarkable similarity between how the bosons and fermions arise in [Formula: see text] theory.