T-duality and non-geometric solutions from double geometry

TL;DR

This paper explores how duality transformations, especially T-duality, can be derived from first principles within double field theory, clarifying their geometric origin and extending the understanding of non-geometric solutions.

Contribution

It provides a first-principles derivation of duality transformations in double geometry by extending gauge symmetry definitions through isometries of a pseudo-Riemannian manifold.

Findings

Derived duality transformations from first principles

Connected gauge symmetries with isometries in extended geometry

Clarified the geometric origin of non-geometric solutions

Abstract

Although the introduction of generalised and extended geometry has been motivated mainly by the appearance of dualities upon reductions on tori, it has until now been unclear how (all) the duality transformations arise from first principles in extended geometry. A proposal for solving this problem is given in the framework of double field theory. It is based on a clearly defined extension of the definition of gauge symmetry by isometries of an underlying pseudo-Riemannian manifold. The ensuing relation between transformations of coordinates and fields, which is now derived from first principles, differs from earlier proposals.