Gravity theory on Poisson manifold with R‐flux. Issue 11 (2nd November 2015) - Asakawa, Tsuguhiko; Muraki, Hisayoshi; Watamura, Satoshi
Abstract : A novel gravity theory based on Poisson Generalized Geometry is investigated. To this end 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. It is shown 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 formulated in the standard Generalized Geometry. An analogue of the Einstein‐Hilbert action coupled with an R ‐flux is given.It turns out to be invariant under both β‐diffeomorphisms and β‐gauge transformations. 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 formulated 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 β‐diffeomorphisms and β‐gauge transformations.