Geometry of T-duality

TL;DR

This paper develops a specialized differential geometry framework for abelian isometries that simplifies T-duality transformations, enabling clearer understanding and covariant corrections of geometrical objects like connections and curvatures.

Contribution

It introduces a reduced differential geometry tailored for abelian isometries, facilitating diagonalization of T-duality and covariant transformation of geometric structures.

Findings

Diagonalization of T-duality in the new geometric setting

Explicit transformation rules for connections and curvatures

Construction of privileged maps for covariant derivatives

Abstract

A "reduced" differential geometry adapted to the presence of abelian isometries is constructed.Classical T-duality diagonalizes in this setting, allowing us to get conveniently the transformation of the relevant geometrical objects such as connections, pullbacks and generalized curvatures.Moreover we can induce privileged maps from the viewpoint of the covariant derivatives in the target-space and in the world-sheet generalizing previous results, at the same time that we can correct connections and curvatures covariantly in order to have a proper transformation under T-duality.