Journal of High Energy Physics (Sep 2020)

Exploring exceptional Drinfeld geometries

  • Chris D. A. Blair,
  • Daniel C. Thompson,
  • Sofia Zhidkova

DOI
https://doi.org/10.1007/JHEP09(2020)151
Journal volume & issue
Vol. 2020, no. 9
pp. 1 – 34

Abstract

Read online

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.

Keywords