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

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.