Gravity theory on Poisson manifold with $R$-flux

TL;DR

This paper develops a gravity theory on Poisson manifolds using Poisson Generalized Geometry, incorporating $R$-fluxes as torsion and establishing an invariant Einstein-Hilbert-like action.

Contribution

It introduces a novel gravity framework on Poisson manifolds with $R$-fluxes, extending generalized geometry concepts to include torsion from $R$-fluxes.

Findings

$R$-fluxes are coupled as torsion in the gravity theory.

The action is invariant under $eta$-diffeomorphisms and $eta$-gauge transformations.

An analogue of Einstein-Hilbert action is formulated with $R$-fluxes.

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.