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

TL;DR

This paper reformulates the structure of double field theory algebroids as curved $L_ olinebreak_ ext{infinity}$-algebras, linking symmetries and constraints to advanced algebraic frameworks for better coordinate invariance.

Contribution

It introduces a novel description of DFT algebroids as curved $L_ ext{infinity}$-algebras and connects the strong constraint to $L_ ext{infinity}$-algebra morphisms, advancing the mathematical foundation of double field theory.

Findings

DFT algebroid is a special case of Vaisman algebroid.

Strong constraint corresponds to an $L_ ext{infinity}$-algebra morphism.

Provides a step towards coordinate-invariant DFT formulations.

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.