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Journal Article

Poisson-Lie U-duality in Exceptional Field Theory


Malek,  Emanuel
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Malek, E., & Thompson, D. C. (2020). Poisson-Lie U-duality in Exceptional Field Theory. Journal of High Energy Physics, 2020(04): 58. doi:10.1007/JHEP04(2020)058.

Cite as: https://hdl.handle.net/21.11116/0000-0005-4D42-B
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.