Poisson-Lie U-duality in Exceptional Field Theory

TL;DR

This paper extends Poisson-Lie duality to M-theory using exceptional field theory, introducing exceptional Drinfeld algebras and defining Poisson-Lie U-duality with potential applications in supergravity solution generation.

Contribution

It generalizes Poisson-Lie duality to M-theory through exceptional Drinfeld algebras and develops a framework for Poisson-Lie U-duality within exceptional field theory.

Findings

Introduction of exceptional Drinfeld algebra structure

Definition of Poisson-Lie U-duality in M-theory

Connection to Yang-Baxter deformations and supergravity solutions

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.