Gravitational theories coupled to matter as invariant theories under Kac-Moody algebras

TL;DR

This paper explores how various gravitational theories coupled with matter fields can be described as invariant under infinite-dimensional Kac-Moody algebras, revealing deep symmetry structures in fundamental physics.

Contribution

It develops a new framework linking gravitational theories to Kac-Moody symmetries, extending the understanding of their algebraic structure and invariance properties.

Findings

Gravitational theories coupled to matter exhibit invariance under G^{++} and G^{+++} Kac-Moody algebras.

Extended symmetries suggest a unifying algebraic description of diverse gravitational models.

The link between these symmetries and uncompactified space-time theories is established.

Abstract

Many recent researches indicate that several gravitational D-dimensional theories suitably coupled to some matter fields (including in particular pure gravity in D dimensions, the low energy effective actions of the bosonic string and the bosonic sector of M-theory) would be characterized by infinite dimensional Kac-Moody algebras G^{++} and G^{+++}. The possible existence of these extended symmetries motivates a development of a new description of gravitational theories based on these symmetries. The importance of Kac-Moody algebras and the link between the G^{+++}-invariant theories and the uncompactified space-time covariant theories are discussed.