# E theory in seven dimensions

## TL;DR

This paper constructs a seven-dimensional theory based on the non-linear realisation of E11, reproducing the equations of motion of seven-dimensional supergravity through algebraic and geometric methods.

## Contribution

It develops a new algebraic framework using E11 and its vector representation to derive seven-dimensional supergravity equations of motion.

## Key findings

- Derived equations match known supergravity equations
- Framework based on E11 Dynkin diagram
- Reproduces standard supergravity fields and dynamics

## Abstract

We construct the non-linear realisation of the semi-direct product of E11 and its vector representation in its decomposition into the subalgebra GL(7)x SL(5) to find a seven dimensional theory. The resulting equations of motion essentially follow from the Dynkin diagram of E11 and if one restricts them to contain only the usual fields of supergravity and the derivatives with respect to the usual coordinates of spacetime then these are the equations of motion of seven dimensional supergravity.