T-Dualities and Courant Algebroid Relations

TL;DR

This paper introduces a unified framework for T-duality using Courant algebroid relations, extending standard T-duality and its generalizations through a geometric approach based on reductions and generalized isometries.

Contribution

It develops a new Courant algebroid relation framework for T-duality, encompassing standard and generalized T-duality, with proofs of existence and uniqueness of related structures.

Findings

Reproduces standard T-duality relations via correspondence spaces

Extends T-duality to almost para-Hermitian manifolds

Provides a unified geometric framework for T-duality

Abstract

We develop a new approach to T-duality based on Courant algebroid relations which subsumes the usual T-duality as well as its various generalisations. Starting from a relational description for the reduction of exact Courant algebroids over foliated manifolds, we introduce a weakened notion of generalised isometries that captures the generalised geometry counterpart of Riemannian submersions when applied to transverse generalised metrics. This is used to construct T-dual backgrounds as generalised metrics on reduced Courant algebroids which are related by a generalised isometry. We prove an existence and uniqueness result for generalised isometric exact Courant algebroids coming from reductions. We demonstrate that our construction reproduces standard T-duality relations based on correspondence spaces. We also describe how it applies to generalised T-duality transformations of almost para-Hermitian manifolds.