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

TL;DR

This paper demonstrates that all intersecting extremal brane solutions in maximally oxidised theories can be exactly described within the G+++ invariant framework, extending to exotic phases and revealing deep algebraic structures.

Contribution

It proves that all extremal brane solutions have algebraic counterparts as exact solutions in G+++ invariant theories, including exotic phases.

Findings

All extremal brane solutions correspond to exact G+++ solutions.

Intersection rules translate into orthogonality conditions on roots.

Extension of proof to exotic phases of theories.

Abstract

The set of exact solutions of the non-linear realisations of the G+++ Kac-Moody algebras is further analysed. Intersection rules for extremal branes translate into orthogonality conditions on the positive real roots characterising each brane. It is proven that all the intersecting extremal brane solutions of the maximally oxidised theories have their algebraic counterparts as exact solutions in the G+++ invariant theories. The proof is extended to include the intersecting extremal brane solutions of the exotic phases of the maximally oxidised theories.