Non-Abelian U-duality for membrane

Abstract

T-duality of string theory can be extended to the Poisson-Lie T-duality when the target space has a generalized isometry group given by a Drinfel'd double. In M-theory, T-duality is understood as a subgroup of U-duality, but the non-Abelian extension of U-duality is still a mystery. In this paper, we study membrane theory on a curved background with a generalized isometry group given by the ${\mathcal{E}}_n$ algebra. This provides a natural setup to study non-Abelian U-duality because the ${\mathcal{E}}_n$ algebra has been proposed as a U-duality extension of the Drinfel'd double. We show that the standard treatment of Abelian U-duality can be extended to the non-Abelian setup. However, a famous issue in Abelian U-duality still exists in the non-Abelian extension.

32 pages; v2: references added, note added, accepted to PTEP

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Cited by in corpus (15)

• E${}_{6(6)}$ Exceptional Drinfel'd Algebras
• Non-abelian tri-vector deformations in d=11 supergravity
• Exploring Exceptional Drinfeld Geometries
• Polyvector deformations in eleven-dimensional supergravity
• Non-abelian U-duality at work
• On non-abelian U-duality of 11D backgrounds
• Global Aspects of Doubled Geometry and Pre-rackoid
• Currents, charges and algebras in exceptional generalised geometry
• Integrability structures in string theory
• Extended Drinfel'd algebras and non-Abelian duality
• Towards an extended/higher correspondence -- Generalised geometry, bundle gerbes and global Double Field Theory
• Poisson-Lie T-plurality for dressing cosets
• Non-isometric U-dualities
• Brane current algebras and generalised geometry from QP manifolds
• Half-maximal Extended Drinfel'd Algebras