Exploring Exceptional Drinfeld Geometries

TL;DR

This paper introduces the Exceptional Drinfeld Algebra, a novel algebraic structure in exceptional generalised geometry, which aids in understanding U-dualities and provides new supergravity uplifts.

Contribution

It defines the Exceptional Drinfeld Algebra, explores its realisation in geometry, and presents examples including three-algebra geometries with applications to supergravity.

Findings

Introduces the Exceptional Drinfeld Algebra as a Leibniz algebra.

Provides explicit examples of three-algebra geometries.

Shows potential for novel uplifts in supergravity theories.

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.