A double field theory algebroid (DFT algebroid) is a special case of the metric (or Vaisman) algebroid, shown to be relevant in understanding the symmetries of double field theory. In particular, a DFT algebroid is a structure defined on a vector bundle over doubled spacetime equipped with the C-bracket of double field theory. In this paper, we give the definition of a DFT algebroid as a curved L_∞-algebra and show how implementation of the strong constraint of double field theory can be formulated as an L_∞-algebra morphism. Our results provide a useful step toward coordinate invariant descriptions of double field theory and the construction of the corresponding sigma-model.

中文翻译：

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双场论代数和弯曲L∞-代数

双场理论代数（DFT algebroid）是度量（或 Vaisman）代数的一个特例，被证明与理解双场理论的对称性有关。特别地，DFT 代数体是定义在双时空上的向量丛上的结构，该结构配备双场论的 C 括号。在本文中，我们将 DFT 代数定义为弯曲的L _{∞ -}代数，并说明如何将双场论的强约束的实现表述为L _{∞ -}代数态射。我们的结果为双场理论的坐标不变描述和相应sigma模型的构建提供了有用的步骤。