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arXiv · 1508.05706

Gravity theory on Poisson manifold with $R$-flux

Tsuguhiko Asakawa·Hisayoshi Muraki·Satoshi Watamura
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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 $β$-diffeomorphisms and $β$-gauge transformations.

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Tsuguhiko Asakawa, Hisayoshi Muraki, Satoshi Watamura. 2015-09-07. Gravity theory on Poisson manifold with $R$-flux. https://doi.org/10.1002/prop.201500049

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