Poisson-generalized geometry and $R$-flux

Understand

We study a new kind of Courant algebroid on Poisson manifolds, which is a variant of the generalized tangent bundle in the sense that the roles of tangent and the cotangent bundle are exchanged.

• Its symmetry is a semidirect product of $\beta$-diffeomorphisms and $\beta$-transformations.
• It is a starting point of an alternative version of the generalized geometry based on the cotangent bundle, such as Dirac structures and generalized Riemannian structures.
• In particular, $R$-fluxes are formulated as a twisting of this Courant algebroid by a local $\beta$-transformations, in the same way as $H$-fluxes are the twist of the generalized tangent bundle.