Poisson-Lie U-duality in Exceptional Field Theory

Abstract

Poisson-Lie duality provides an algebraic extension of conventional Abelian and non-Abelian target space dualities of string theory and has seen recent applications in constructing quantum group deformations of holography. Here we demonstrate a natural upgrading of Poisson-Lie to the context of M-theory using the tools of exceptional field theory. In particular, we propose how the underlying idea of a Drinfeld double can be generalised to an algebra we call an exceptional Drinfeld algebra. These admit a notion of "maximally isotropic subalgebras" and we show how to define a generalised Scherk-Schwarz truncation on the associated group manifold to such a subalgebra. This allows us to define a notion of Poisson-Lie U-duality. Moreover, the closure conditions of the exceptional Drinfeld algebra define natural analogues of the cocycle and co-Jacobi conditions arising in Drinfeld double. We show that upon making a further coboundary restriction to the cocycle that an M-theoretic extension of Yang-Baxter deformations arise. We remark on the application of this construction as a solution-generating technique within supergravity.

arXiv comment20 pages; v2: minor changes made, references added

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• E${}_{6(6)}$ Exceptional Drinfel'd Algebras
• Generalized Dualities and Higher Derivatives
• Non-Abelian U-duality for membrane
• Non-abelian tri-vector deformations in d=11 supergravity
• Exploring Exceptional Drinfeld Geometries
• Polyvector deformations in eleven-dimensional supergravity
• G-algebroids: a unified framework for exceptional and generalised geometry, and Poisson-Lie duality
• Non-abelian U-duality at work
• On non-abelian U-duality of 11D backgrounds
• Consistent Truncations and Dualities
• Global Aspects of Doubled Geometry and Pre-rackoid
• Exceptional algebroids and type IIB superstrings
• All maximal gauged supergravities with uplift
• Currents, charges and algebras in exceptional generalised geometry
• Generalized Dualities and Supergroups
• More on Doubled Aspects of Algebroids in Double Field Theory
• Jacobi-Lie T-plurality
• Tri-vector deformations on compact isometries
• Generalised U-dual solutions via ISO(7) gauged supergravity
• Polyvector deformations of Type IIB backgrounds
• Integrability structures in string theory
• On 10 dimensional Exceptional Drinfel'd Algebras
• Towards an extended/higher correspondence -- Generalised geometry, bundle gerbes and global Double Field Theory
• Y-algebroids and $E_{7(7)}\times {\mathbb{R}}^{+}$-generalised geometry
• Poisson-Lie T-plurality for dressing cosets
• Jacobi-Lie Models and Supergravity Equations
• T-folds as Poisson-Lie plurals
• Tri-vector deformations with external fluxes
• Classification of six-dimensional Leibniz algebras ${\mathcal E}_3
• Extended Doubled Structures of Algebroids for Gauged Double Field Theory
• Non-isometric U-dualities
• Exceptional algebroids and type IIA superstrings
• Generalised U-dual solutions in supergravity