G-algebroids: a unified framework for exceptional and generalised geometry, and Poisson-Lie duality

Abstract

We introduce the notion of G-algebroid, generalising both Lie and Courant algebroids, as well as the algebroids used in $E_{n(n)}\times {\mathbb{R}}^{+}$ exceptional generalised geometry for $n\in \{3,\dots ,6\}$. Focusing on the exceptional case, we prove a classification of "exact" algebroids and translate the related classification of Leibniz parallelisable spaces into a tractable algebraic problem. After discussing the general notion of Poisson-Lie duality, we show that the Poisson-Lie U-duality is compatible with the equations of motion of supergravity.

17 pages, updated references

References in corpus (19)

• Generalized metric formulation of double field theory
• Superspace Duality in Low-Energy Superstrings
• Dual Non-Abelian Duality and the Drinfeld Double
• Generalised Geometry for M-Theory
• Supergravity as Generalised Geometry I: Type II Theories
• M-theory, exceptional generalised geometry and superpotentials
• The gauge structure of generalised diffeomorphisms
• Differential geometry with a projection: Application to double field theory
• Poisson-Lie T-Duality in Double Field Theory
• Torsion-free generalized connections and Heterotic Supergravity
• Leibniz algebroids, twistings and exceptional generalized geometry
• U-duality extension of Drinfel'd double
• Poisson-Lie U-duality in Exceptional Field Theory
• Generalised Scherk-Schwarz reductions from gauged supergravity
• One loop renormalizability of the Poisson-Lie sigma models
• Poisson-Lie T-duality and Courant algebroids
• Ricci flow, Courant algebroids, and renormalization of Poisson--Lie T-duality
• Generalized Parallelizable Spaces from Exceptional Field Theory
• Subsectors, Dynkin Diagrams and New Generalised Geometries

Cited by in corpus (10)

• Exceptional algebroids and type IIB superstrings
• The higher-dimensional origin of five-dimensional $\mathcal{N}=2$ gauged supergravities
• All maximal gauged supergravities with uplift
• Maximal D=2 supergravities from higher dimensions
• Poisson-Lie T-plurality for dressing cosets
• Y-algebroids and $E_{7(7)}\times {\mathbb{R}}^{+}$-generalised geometry
• Non-isometric U-dualities
• Extended Doubled Structures of Algebroids for Gauged Double Field Theory
• Exceptional algebroids and type IIA superstrings
• Generalised U-dual solutions in supergravity