Algebroids, AKSZ Constructions and Doubled Geometry

Abstract We give a self-contained survey of some approaches aimed at global description the geometry underlying double field theory. After reviewing Courant algebroids and their incarnations in AKSZ construction, we develop theory metric including graded geometry. use to doubled geometry, incorporating section constraint, as well an AKSZ-type construction topological sigma-models. When these notions are combined with ingredients para-Hermitian demonstrate how they reproduce kinematical features from perspective, solutions constraint for Riemannian foliated manifolds, natural notion generalized T-duality polarized manifolds. describe L ? -algebras symmetries briefly discuss other proposals literature.