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arXiv · 1203.0836

On the geometry of double field theory

Izu Vaisman
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Abstract

Double field theory was developed by theoretical physicists as a way to encompass $T$-duality. In this paper, we express the basic notions of the theory in differential-geometric invariant terms, in the framework of para-Kaehler manifolds. We define metric algebroids, which are vector bundles with a bracket of cross sections that has the same metric compatibility property as a Courant bracket. We show that a double field gives rise to two canonical connections, whose scalar curvatures can be integrated to obtain actions. Finally, in analogy with Dirac structures, we define and study para-Dirac structures on double manifolds.

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Izu Vaisman. 2012-03-05. On the geometry of double field theory. https://doi.org/10.1063/1.3694739

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