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.

arXiv comment30 pages, 1 figure, version published in JHEP

References in corpus (38)

• Double Field Theory
• Generalized metric formulation of double field theory
• Superspace Duality in Low-Energy Superstrings
• Two-Vierbein Formalism for String-Inspired Axionic Gravity
• Duality Symmetries from Non--Abelian Isometries in String Theories
• Dual Non-Abelian Duality and the Drinfeld Double
• The gauge algebra of double field theory and Courant brackets
• Reduction of Courant algebroids and generalized complex structures
• Lectures on Gauged Supergravity and Flux Compactifications
• Gauged Double Field Theory
• $L_{\infty }$ Algebras and Field Theory
• Double Field Theory Formulation of Heterotic Strings
• Gauged Supergravities
• Generalised geometry for string corrections
• Poisson-Lie T-Duality in Double Field Theory
• Torsion-free generalized connections and Heterotic Supergravity
• Generalized Calabi-Yau manifolds
• Poisson-Lie T-plurality
• Leibniz algebroids, twistings and exceptional generalized geometry
• On the geometry of double field theory
• Towards a double field theory on para-Hermitian manifolds
• Double Field Theory and Membrane Sigma-Models
• Poisson-Lie U-duality in Exceptional Field Theory
• A Unique Connection for Born Geometry
• Generalised Kinematics for Double Field Theory
• Type II DFT solutions from Poisson-Lie T-duality/plurality
• Algebroid Structures on Para-Hermitian Manifolds
• Para-Hermitian Geometry, Dualities and Generalized Flux Backgrounds
• G-algebroids: a unified framework for exceptional and generalised geometry, and Poisson-Lie duality
• Non-abelian U-duality at work
• Doubled Aspects of Vaisman Algebroid and Gauge Symmetry in Double Field Theory
• Global Aspects of Doubled Geometry and Pre-rackoid
• Courant sigma model and $L_{\infty }$-algebras
• Double field theory algebroid and curved $L_{\infty }$-algebras
• More on Doubled Aspects of Algebroids in Double Field Theory
• Jacobi-Lie T-plurality
• Metric algebroid and Dirac generating operator in Double Field Theory
• Metric Algebroid and Poisson-Lie T-duality in DFT