Strings in Spacetime Cotangent Bundle and T-duality

TL;DR

This paper presents a geometric framework for T-duality using cotangent bundles, showing that dual string phase spaces are related by a symplectomorphism, simplifying the understanding of T-duality transformations.

Contribution

It introduces a geometric description of T-duality via cotangent bundles, providing a clear, projective derivation of Buscher's transformation and proving duality as a symplectomorphism.

Findings

T-duality can be described by cotangent bundle identification.

Buscher's transformation is projective and straightforward.

Dual string phase spaces are symplectomorphic.

Abstract

A simple geometric description of T-duality is given by identifying the cotangent bundles of the original and the dual manifold. Strings propagate naturally in the cotangent bundle and the original and the dual string phase spaces are obtained by different projections. Buscher's transformation follows readily and it is literally projective. As an application of the formalism, we prove that the duality is a symplectomorphism of the string phase spaces.