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A brief review of E theory

Peter West

Department of Mathematics, King’s College, London WC2R 2LS, UK

https://doi.org/10.1142/S0217751X1630043XCited by:10

Abstract

I begin with some memories of Abdus Salam who was my PhD supervisor. After reviewing the theory of nonlinear realisations and Kac–Moody algebras, I explain how to construct the nonlinear realisation based on the Kac–Moody algebra $E_{11}$ 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 11-dimensional supergravity theory. By taking different group decompositions of $E_{11}$ we find all the maximal supergravity theories, including the gauged maximal supergravities, and as a result the nonlinear 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 $E_{11}$ conjecture given many years ago.

Based on an invited talk given at the Memorial Meeting for Nobel Laureate Prof. Abdus Salam’s 90th Birthday, 25–28 January 2016, NTU, Singapore.

Keywords:

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A brief review of E theory

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