Transitive Courant Algebroids, String Structures and T-duality

TL;DR

This paper explores how T-duality interacts with transitive Courant algebroids and string structures, establishing conditions for T-duals in heterotic string theory and deriving related transformations and equations.

Contribution

It introduces a method to construct transitive Courant algebroids from string classes and shows T-duality exchanges string structures, extending its applicability.

Findings

T-duality commutes with reductions of Courant algebroids.

String structures are exchanged under T-duality.

Heterotic Einstein equations are preserved under T-duality.

Abstract

In this paper, we use reduction by extended actions to give a construction of transitive Courant algebroids from string classes. We prove that T-duality commutes with the reductions and thereby determine global conditions for the existence of T-duals in heterotic string theory. In particular we find that T-duality exchanges string structures and gives an isomorphism of transitive Courant algebroids. Consequently we derive the T-duality transformation for generalised metrics and show that the heterotic Einstein equations are preserved. The presence of string structures significantly extends the domain of applicability of T-duality and this is illustrated by several classes of examples.