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arXiv · 1802.08180

Algebroid Structures on Para-Hermitian Manifolds

David Svoboda
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Abstract

We present a global construction of a so-called D-bracket appearing in the physics literature of Double Field Theory (DFT) and show that if certain integrability criteria are satisfied, it can be seen as a sum of two Courant algebroid brackets. In particular, we show that the local picture of the extended space-time used in DFT fits naturally in the geometrical framework of para-Hermitian manifolds and that the data of an (almost) para-Hermitian manifold is sufficient to construct the D-bracket. Moreover, the twists of the bracket appearing in DFT can be interpreted in this framework geometrically as a consequence of certain deformations of the underlying para-Hermitian structure.

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David Svoboda. 2019-12-16. Algebroid Structures on Para-Hermitian Manifolds. https://doi.org/10.1063/1.5040263

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