Hitchhiker's Guide to Courant Algebroid Relations

TL;DR

This paper develops a comprehensive framework for Courant algebroid relations and morphisms, emphasizing their applications in string theory, Poisson-Lie T-duality, and supergravity reductions, with detailed examples and motivations.

Contribution

It introduces a more general notion of Courant algebroid relations beyond previous symplectic analogues, tailored for physics applications.

Findings

Courant algebroid relations can model generalized isometries in string theory.

Poisson-Lie T-duality is interpretable as a Courant algebroid relation.

Kaluza-Klein reduction of supergravity fits into the Courant algebroid framework.

Abstract

Courant algebroids provide a useful mathematical tool (not only) in string theory. It is thus important to define and examine their morphisms. To some extent, this was done before using an analogue of canonical relations known from symplectic geometry. However, it turns out that applications in physics require a more general notion. We aim to provide a self-contained and detailed treatment of Courant algebroid relations and morphisms. A particular emphasis is placed on providing enough motivating examples. In particular, we show how Poisson-Lie T-duality and Kaluza-Klein reduction of supergravity can be interpreted as Courant algebroid relations compatible with generalized metrics (generalized isometries).