Extended Doubled Structures of Algebroids for Gauged Double Field Theory

Abstract

We study an analogue of the Drinfel'd double for algebroids associated with the $O(D,D+n)$ gauged double field theory (DFT). We show that algebroids defined by the twisted C-bracket in the gauged DFT are built out of a direct sum of three (twisted) Lie algebroids. They exhibit a "tripled", which we call the extended double, rather than the "doubled" structure appeared in (ungauged) DFT. We find that the compatibilities of the extended doubled structure result not only in the strong constraint but also the additional condition in the gauged DFT. We establish a geometrical implementation of these structures in a $(2D+n)$-dimensional product manifold and examine the relations to the generalized geometry for heterotic string theories and non-Abelian gauge symmetries in DFT.

30 pages, 1 figure, version published in JHEP

References in corpus (9)

• Double Field Theory
• The gauge algebra of double field theory and Courant brackets
• Lectures on Gauged Supergravity and Flux Compactifications
• Gauged Double Field Theory
• Double Field Theory Formulation of Heterotic Strings
• Generalised Kinematics for Double Field Theory
• G-algebroids: a unified framework for exceptional and generalised geometry, and Poisson-Lie duality
• Jacobi-Lie T-plurality
• Metric Algebroid and Poisson-Lie T-duality in DFT