Gravity theory on Poisson manifold with $R$-flux

Abstract

A novel gravity theory based on Poisson Generalized Geometry is investigated. A gravity theory on a Poisson manifold equipped with a Riemannian metric is constructed from a contravariant version of the Levi-Civita connection, which is based on the Lie algebroid of a Poisson manifold. Then, we show that in Poisson Generalized Geometry the $R$-fluxes are consistently coupled with such a gravity. An $R$-flux appears as a torsion of the corresponding connection in a similar way as an $H$-flux which appears as a torsion of the connection for- mulated in the standard Generalized Geometry. We give an analogue of the Einstein-Hilbert action coupled with an $R$-flux, and show that it is invariant under both $\beta$-diffeomorphisms and $\beta$-gauge transformations.

37 pages, Some comments and references added

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Cited by in corpus (10)

• Weaving the Exotic Web
• Semi-doubled Sigma Models for Five-branes
• Heterotic Reduction of Courant Algebroid Connections and Einstein-Hilbert Actions
• Finite Transformations in Doubled and Exceptional Space
• The BV action of 3D twisted R-Poisson sigma models
• Deformed graded Poisson structures, Generalized Geometry and Supergravity
• Contravariant Gravity on Poisson Manifolds and Einstein Gravity
• Killing sections and sigma models with Lie algebroid targets
• Contravariant geometry and emergent gravity from noncommutative gauge theories
• A gravitational action with stringy $Q$ and $R$ fluxes via deformed differential graded Poisson algebras