Coset Symmetries in Dimensionally Reduced Bosonic String Theory

TL;DR

This paper explores the symmetry structures arising from dimensional reduction of bosonic string theory and gravity, revealing coset symmetries and connections to Kac-Moody algebras, with implications for M-theory.

Contribution

It demonstrates the emergence of coset symmetries in reduced bosonic string theory and links to the Geroch group and Kac-Moody algebras, extending the understanding of duality symmetries.

Findings

Coset symmetries match recent predictions in reduced bosonic string theory.

Part of the Geroch group appears in the duality symmetric gravity formulation.

Proposes a Kac-Moody algebra extension for the non-linear realization.

Abstract

We discuss the dimensional reduction of various effective actions, particularly that of the closed Bosonic string and pure gravity, to two and three dimensions. The result for the closed Bosonic string leads to coset symmetries which are in agreement with those recently predicted and argued to be present 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 extended to a non-linear realisation based on a Kac-Moody algebra which we identify. We also briefly discuss the proposed action of Bosonic M-theory.