Double field theory algebroid and curved $L_\infty$-algebras

Clay James Grewcoe; Larisa Jonke

doi:10.1063/5.0041479

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arXiv · 2012.02712

Double field theory algebroid and curved $L_\infty$-algebras

Clay James Grewcoe·Larisa Jonke

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Abstract

A 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 $L_\infty$-algebra and show how implementation of the strong constraint of double field theory can be formulated as an $L_\infty$-algebra morphism. Our results provide a useful step towards coordinate invariant descriptions of double field theory and the construction of the corresponding sigma-model.

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Clay James Grewcoe, Larisa Jonke. 2021-06-29. Double field theory algebroid and curved $L_\infty$-algebras. https://doi.org/10.1063/5.0041479

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