The Symmetry of M-Theories

TL;DR

This paper explores the deep algebraic structures underlying theories of gravity and matter, revealing that very extended algebras encode symmetries like dualities and may be fundamental to constructing consistent physical theories.

Contribution

It demonstrates that very extended algebras G+++ naturally incorporate classical solutions, dualities, and symmetries relevant to gravity and string theories, suggesting a unifying algebraic framework.

Findings

Classical solutions carry Weyl group representations.

T and S-dualities correspond to algebra automorphisms.

Very extended algebras potentially underpin all consistent gravity-matter theories.

Abstract

We consider the Cartan subalgebra of any very extended algebra G+++ where G is a simple Lie algebra and let the parameters be space-time fields. These are identified with diagonal metrics and dilatons. Using the properties of the algebra, we find that for all very extensions G+++ of simple Lie algebras there are theories of gravity and matter, which admit classical solutions carrying representations of the Weyl group of G+++. We also identify the T and S-dualities of superstrings and of the bosonic string with Weyl reflections and outer automorphisms of well-chosen very extended algebras and we exhibit specific features of the very extensions. We take these results as indication that very extended algebras underlie symmetries of any consistent theory of gravity and matter, and might encode basic information for the construction of such theory.