Abstract
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.
Highlights
Introduction and overviewDouble field theory (DFT) is a field theory defined on a double, 2d-dimensional configuration space where the extra coordinates are introduced in an effort to realise T-duality of string theory as a symmetry of field theory [1,2,3,4]
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
The important observation is that the symmetric bilinear on the bundle induces a symmetric pairing on the doubled configuration space, which allows for the appropriate geometric description of a DFT algebroid
Summary
Double field theory (DFT) is a field theory defined on a double, 2d-dimensional configuration space where the extra coordinates are introduced in an effort to realise T-duality of string theory as a symmetry of field theory [1,2,3,4]. The question that naturally arises is if one can provide a geometric description of DFT symmetries based on the C-bracket, before reducing the theory by imposing the strong constraint. Motivated by the observation that in double field theory one doubles the configuration space, while in a Courant algebroid one extends the bundle, in Ref. The important observation is that the symmetric bilinear on the bundle induces a symmetric pairing on the doubled configuration space, which allows for the appropriate geometric description of a DFT algebroid. This pairing is a para-Hermitan metric on the doubled configuration space, see Refs.
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