G+++ Invariant Formulation of Gravity and M-Theories: Exact BPS Solutions

TL;DR

This paper proposes a unified algebraic framework for gravity and M-theories using G+++ Kac-Moody algebras, deriving exact solutions that describe BPS branes and dualities, and suggesting space-time emergence from algebraic structures.

Contribution

It introduces a G+++ invariant formulation of gravity and M-theories, including exact solutions and a novel perspective on dualities and space-time emergence.

Findings

Exact solutions for all G+++ algebras describing BPS branes and Kaluza-Klein objects.

Demonstration of duality as Weyl invariance within G+++ algebraic structure.

Proposal that space-time arises dynamically from algebraic generators.

Abstract

We present a tentative formulation of theories of gravity with suitable matter content, including in particular pure gravity in D dimensions, the bosonic effective actions of M-theory and of the bosonic string, in terms of actions invariant under very-extended Kac-Moody algebras G+++. We conjecture that they host additional degrees of freedom not contained in the conventional theories. The actions are constructed in a recursive way from a level expansion for all very-extended algebras G+++. They constitute non-linear realisations on cosets, a priori unrelated to space-time, obtained from a modified Chevalley involution. Exact solutions are found for all G+++. They describe the algebraic properties of BPS extremal branes, Kaluza-Klein waves and Kaluza-Klein monopoles. They illustrate the generalisation to all G+++ invariant theories of the well-known duality properties of string theories by expressing duality as Weyl invariance in G+++. Space-time is expected to be generated dynamically. In the level decomposition of E8+++ = E11, one may indeed select an A10 representation of generators Pa which appears to engender space-time translations by inducing infinite towers of fields interpretable as field derivatives in space and time.