E_{11} and Higher Spin Theories

TL;DR

This paper explores an extension of spacetime based on E_{11} symmetry, proposing a framework that naturally incorporates an infinite tower of higher spin fields through a non-linear realisation.

Contribution

It introduces a novel approach using E_{11} to generate a unified description of higher spin theories via a generalized spacetime and symmetry structure.

Findings

Determines symmetries for a point particle in the generalized spacetime.

Constructs an action consistent with these symmetries.

Argues that the framework leads to an infinite spectrum of higher spin fields.

Abstract

We consider the previous proposal of the author to use an extension of spacetime obtained by taking the non-linear realisation of the semi-direct product of E_{11} with a set of generators belonging to one of the fundamental representations of E_{11}. We determine, at low levels, the symmetries that the associated point particle moving in this generalised spacetime should possess and write down the corresponding action. Quantisation of similar actions has been shown to lead to the unfolded formulation of higher spin theories and we argue that the generalised coordinates will lead in the non-linear realisation to an infinite number of propagating higher spin fields.