From brane dynamics to a Kac-Moody invariant formulation of M-theories

Abstract

Theories of gravity coupled to forms and dilatons may admit as solutions zero binding energy configurations of intersecting closed extremal branes. In such configurations, some branes may open on host closed branes. Properties of extremal branes reveal symmetries of the underlying theory which are well known in M-theory but transcend supersymmetry. From these properties it is possible to reconstruct all actions, comprising in particular pure gravity in D dimensions, the bosonic effective actions of M-theory and of the bosonic string, which upon dimensional reduction to three dimensions are invariant under the maximally non-compact simple simply laced Lie groups G. Moreover the features of extremal branes suggest the existence of a much larger symmetry, namely the `very-extended' Kac-Moody algebras G+++. This motivates the construction of explicit non-linear realisations of all simple G+++, which hopefully contain new degrees of freedom such as those encountered in string theories. They are defined without a priori reference to space-time and are proposed as substitutes for original field theoretic models of gravity, forms and dilatons. From the G+++ invariant theories, all algebraic properties of extremal branes are recovered from exact solutions, and there are indications that space-time is hidden in the infinite symmetry structure. The transformation properties of the exact solutions, which possibly induce new solutions foreign to conventional theories, put into evidence the general group-theoretical origin of `dualities' for all G+++. These dualities apparently do not require an underlying string theory.