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arXiv · 1408.2649

Poisson-generalized geometry and $R$-flux

T. Asakawa·H. Muraki·S. Sasa·S. Watamura
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Abstract

We study a new kind of Courant algebroid on Poisson manifolds, which is a variant of the generalized tangent bundle in the sense that the roles of tangent and the cotangent bundle are exchanged. Its symmetry is a semidirect product of $\beta$-diffeomorphisms and $\beta$-transformations. It is a starting point of an alternative version of the generalized geometry based on the cotangent bundle, such as Dirac structures and generalized Riemannian structures. In particular, $R$-fluxes are formulated as a twisting of this Courant algebroid by a local $\beta$-transformations, in the same way as $H$-fluxes are the twist of the generalized tangent bundle. It is a $3$-vector classified by Poisson $3$-cohomology and it appears in a twisted bracket and in an exact sequence.

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T. Asakawa, H. Muraki, S. Sasa, S. Watamura. 2014-08-12. Poisson-generalized geometry and $R$-flux. https://doi.org/10.1142/s0217751x15500979

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