Poisson-generalized geometry and $R$-flux

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.

22 pages

References in corpus (5)

• T-duality for principal torus bundles
• Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids
• D-branes in Generalized Geometry and Dirac-Born-Infeld Action
• Dirac structures on nilmanifolds and coexistence of fluxes
• D-brane on Poisson manifold and Generalized Geometry

Cited by in corpus (10)

• Unified picture of non-geometric fluxes and T-duality in double field theory via graded symplectic manifolds
• Pre-Courant Algebroids
• Double field theory for the A/B-models and topological S-duality in generalized geometry
• Gravity theory on Poisson manifold with $R$-flux
• Semi-doubled Sigma Models for Five-branes
• Fluxes in Exceptional Field Theory and Threebrane Sigma-Models
• Contravariant Gravity on Poisson Manifolds and Einstein Gravity
• Topological Membranes, Current Algebras and H-flux - R-flux Duality based on Courant Algebroids
• Topological T-duality via Lie algebroids and $Q$-flux in Poisson-generalized geometry
• Contravariant geometry and emergent gravity from noncommutative gauge theories