Coset symmetries in dimensionally reduced bosonic string theory

We discuss the dimensional reduction of various effective actions, particul arly that of the closed bosonic string and pure gravity, to two and three d imensions. The result for the closed bosonic string leads to coset symmetri es which are in agreement with those recently predicted and argued to be pr esent in a new unreduced formulation of this theory. We also show that part of the Geroch group appears in the unreduced duality symmetric formulation of gravity recently proposed. We conjecture that this formulation can be e xtended to a non-linear realisation based on a Kac-Moody algebra which we i dentify. We also briefly discuss the proposed action of bosonic M-theory. ( C) 2001 Elsevier Science B.V. All rights reserved.