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

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.

26 pages; v2: Minor modifications to match the published version, typo corrected

References in corpus (7)

• Double Field Theory
• The gauge algebra of double field theory and Courant brackets
• Letters to Alan Weinstein about Courant algebroids
• Generalised Kinematics for Double Field Theory
• Presymplectic AKSZ formulation of Einstein gravity
• More on Doubled Aspects of Algebroids in Double Field Theory
• The Algebroid Structure of Double Field Theory

Cited by in corpus (4)

• Topological Field Theories induced by twisted R-Poisson structure in any dimension
• Extended Doubled Structures of Algebroids for Gauged Double Field Theory
• Generalized symmetries as homotopy Lie algebras
• Instances of Higher Geometry in Field Theory