Gravity theory on Poisson manifold with $R$-flux

Understand

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.