E11, generalised space-time and equations of motion in four dimensions

TL;DR

This paper develops a framework based on E11 symmetry to describe gravity, scalars, and gauge fields in four dimensions using a generalized space-time that includes additional coordinates, leading to equations of motion consistent with known physics.

Contribution

It constructs a non-linear realization of E11 and its fundamental representation in four dimensions, incorporating a generalized space-time with novel coordinates and deriving unique first-order equations of motion.

Findings

Correctly reproduces equations of motion for scalars and gauge fields

Introduces a generalized space-time with 56 additional coordinates

Demonstrates equations are uniquely determined by E11 algebra properties

Abstract

We construct the non-linear realisation of the semi-direct product of E11 and its first fundamental representation at low levels in four dimensions. We include the fields for gravity, the scalars and the gauge fields as well as the duals of these fields. The generalised space-time, upon which the fields depend, consists of the usual coordinates of four dimensional space-time and Lorentz scalar coordinates which belong to the 56-dimensional representation of E7. We demand that the equations of motion are first order in derivatives of the generalised space-time and then show that they are essentially uniquely determined by the properties of the E11 Kac-Moody algebra and its first fundamental representation. The two lowest equations correctly describe the equations of motion of the scalars and the gauge fields once one takes the fields to depend only on the usual four dimensional space-time.