Poisson-generalized geometry and $R$-flux

TL;DR

This paper introduces a novel Courant algebroid on Poisson manifolds that exchanges tangent and cotangent roles, leading to an alternative generalized geometry framework incorporating $R$-fluxes as twists.

Contribution

It develops a new Courant algebroid structure on Poisson manifolds, defining $R$-fluxes via $eta$-transformations, and establishes an alternative generalized geometry based on the cotangent bundle.

Findings

Defines a new Courant algebroid on Poisson manifolds.

Formulates $R$-fluxes as twists classified by Poisson 3-cohomology.

Provides a twisted bracket and exact sequence involving $R$-fluxes.

Abstract

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. It is a $3$-vector classified by Poisson $3$-cohomology and it appears in a twisted bracket and in an exact sequence.