Hitchhiker's guide to Courant algebroid relations
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 selfcontained and detailed treatment of Courant algebroid relations and morphisms. A particular emphasis is placed on providing enough motivating examples. In particular, we show how PoissonLie Tduality and KaluzaKlein reduction of supergravity can be interpreted as Courant algebroid relations compatible with generalized metrics (generalized isometries).
 Publication:

Journal of Geometry and Physics
 Pub Date:
 May 2020
 DOI:
 10.1016/j.geomphys.2020.103635
 arXiv:
 arXiv:1910.05347
 Bibcode:
 2020JGP...15103635V
 Keywords:

 Courant algebroids;
 Involutive subbundles;
 Canonical relations;
 Symplectic category;
 Reduction of Courant algebroids;
 PoissonLie Tduality;
 Mathematics  Differential Geometry;
 High Energy Physics  Theory;
 Mathematics  Symplectic Geometry
 EPrint:
 Some minor things tweaked, typos corrected, references added