A brief review of E theory

TL;DR

This paper reviews the E11 non-linear realisation, showing how it unifies various supergravity theories and supports the conjecture that E11 underpins low-energy string and brane effective actions.

Contribution

It demonstrates how the E11 algebra leads to equations of motion for eleven-dimensional supergravity and all maximal supergravities through specific group decompositions.

Findings

E11-based dynamical equations reproduce 11D supergravity.

Different group decompositions yield all maximal supergravity theories.

Supports E11 as a unifying framework for string and brane effective actions.

Abstract

I begin with some memories of Abdus Salam who was my PhD supervisor. After reviewing the theory of non-linear realisations and Kac-Moody algebras, I explain how to construct the non-linear realisation based on the Kac-Moody algebra E11 and its vector representation. I explain how this field theory leads to dynamical equations which contain an infinite number of fields defined on a space time with an infinite number of coordinates. I then show that these unique dynamical equations, when truncated to low level fields and the usual coordinates of space time, lead to precisely the equations of motion of eleven dimensional supergravity theory. By taking different group decompositions of E11 we find all the maximal supergravity theories, including the gauged maximal supergravities, and as a result the non-linear realisation should be thought of as a unified theory that is the low energy effective action for type II strings and branes. These results essentially confirm the E11 conjecture given many years ago.