From very-extended to overextended gravity and M-theories

TL;DR

This paper explores the formulation of gravity and M-theories using very-extended Kac-Moody algebras, revealing dualities, exact solutions, and signatures, thereby providing insights into the infinite field structures in these theories.

Contribution

It introduces two distinct G+++ invariant actions with different signatures and demonstrates their exact solutions and dualities, advancing the understanding of Kac-Moody formulations of gravity and M-theories.

Findings

Two invariant actions with Euclidean and Lorentzian signatures are formulated.

Exact solutions describe intersecting extremal branes with duality relations.

Kac-Moody theories share solutions with space-time covariant theories, enabling analysis of infinite fields.

Abstract

The formulation of gravity and M-theories as very-extended Kac-Moody invariant theories encompasses, for each very-extended algebra G+++, two distinct actions invariant under the overextended Kac-Moody subalgebra G++. The first carries a Euclidean signature and is the generalisation to G++ of the E10-invariant action proposed in the context of M-theory and cosmological billiards. The second action carries various Lorentzian signatures revealed through various equivalent formulations related by Weyl transformations of fields. It admits exact solutions, identical to those of the maximally oxidised field theories and of their exotic counterparts, which describe intersecting extremal branes smeared in all directions but one. The Weyl transformations of G++ relates these solutions by conventional and exotic dualities. These exact solutions, common to the Kac-Moody theories and to space-time covariant theories, provide a laboratory for analysing the significance of the infinite set of fields appearing in the Kac-Moody formulations.