T-Dualities and Courant Algebroid Relations

Author:

Thomas C. De Fraja, Vincenzo Emilio Marotta, Richard J. Szabo

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), High Energy Physics - Theory (hep-th), Mathematical Physics (math-ph)

journal:

EMPG-23-12

date:

2023-08-28 16:00:00

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.

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