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

TL;DR

This paper explores the massless irreducible representation in E theory, revealing how duality relations and algebraic structures influence the degrees of freedom and the emergence of bosons as spinors.

Contribution

It provides a detailed analysis of the irreducible representation in E theory, highlighting the role of duality relations and algebraic ideals in shaping particle degrees of freedom.

Findings

128 physical states in the spinor representation of SO(16)

Duality relations reduce degrees of freedom

Bosons can appear as spinors in E theory

Abstract

We study in detail the irreducible representation of E theory that corresponds to massless particles. This has little algebra Ic(E9) and contains 128 physical states that belong to the spinor representation of SO(16). 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 Ic(E9) 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 E theory.