Intersection rules, dynamics and symmetries

TL;DR

This paper explores how intersecting extremal brane solutions in certain gravity theories reveal underlying Lie group symmetries and algebraic structures, connecting brane dynamics to fundamental symmetries in M-theory and string theory.

Contribution

It demonstrates that BPS intersecting brane solutions determine the symmetry groups of reduced theories and relate to the algebraic structure of Kac-Moody extensions, offering a new perspective on theory reconstruction.

Findings

BPS solutions select theories with specific Lie group symmetries.

Brane dynamics encode the algebraic structure of G+++ Kac-Moody extensions.

The algebraic structures differ from those governing cosmological solutions.

Abstract

We consider theories containing gravity, at most one dilaton and form field strengths. We show that the existence of particular BPS solutions of intersecting extremal closed branes select the theories, which upon dimensional reduction to three dimensions possess a simple simply laced Lie group symmetry G. Furthermore these theories can be fully reconstructed from the dynamics of such branes and of their openings. Amongst such theories are the effective actions of the bosonic sector of M-theory and of the bosonic string. The BPS intersecting brane solutions form representations of a subgroup of the group of Weyl reflections and outer automorphisms of the triple Kac-Moody extension G+++ of the G algebra, which cannot be embedded in the overextended Kac-Moody subalgebra G++ characterising the cosmological Kasner solutions.