Exploring Exceptional Drinfeld Geometries

Abstract

We explore geometries that give rise to a novel algebraic structure, the Exceptional Drinfeld Algebra, which has recently been proposed as an approach to study generalised U-dualities, similar to the non-Abelian and Poisson-Lie generalisations of T-duality. This algebra is generically not a Lie algebra but a Leibniz algebra, and can be realised in exceptional generalised geometry or exceptional field theory through a set of frame fields giving a generalised parallelisation. We provide examples including "three-algebra geometries", which encode the structure constants for three-algebras and in some cases give novel uplifts for $CSO(p,q,r)$ gaugings of seven-dimensional maximal supergravity. We also discuss the M-theoretic embedding of both non-Abelian and Poisson-Lie T-duality.

arXiv comment24 pages + appendices + refs. v2: published version

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Cited by in corpus (17)

• E${}_{6(6)}$ Exceptional Drinfel'd Algebras
• Non-abelian U-duality at work
• On non-abelian U-duality of 11D backgrounds
• Exceptional algebroids and type IIB superstrings
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• Towards an extended/higher correspondence -- Generalised geometry, bundle gerbes and global Double Field Theory
• Poisson-Lie T-plurality for dressing cosets
• Jacobi-Lie Models and Supergravity Equations
• Y-algebroids and $E_{7(7)}\times {\mathbb{R}}^{+}$-generalised geometry
• Non-isometric U-dualities
• Generalised U-dual solutions in supergravity
• Exceptional algebroids and type IIA superstrings