Non-abelian U-duality at work

Abstract

Non-abelian U-duality originates from the construction of exceptional Drinfel'd algebra (EDA), which extends the constriction of the classical Drinfel'd double. This symmetry is a natural extension of Poisson--Lie T-duality and is believed to be a symmetry of Type II string/M-theory or their low-energy effective theories. In this paper, we consider non-abelian U-dualities of 11- or 10-dimensional backgrounds starting with E${}_{n(n)}$ EDA with $n\le 6$ with vanishing trombone gauging. The latter guarantees that all dual backgrounds satisfy the standard supergravity equations of motion. In particular, when the duality includes a timelike T-duality, we obtain solutions of M${}^{\ast }$-theory or Type II${}^{\ast }$ background equations, as expected. Also starting with coboundary EDA's we provide examples of generalised Yang--Baxter deformations of M-theory and Type IIB backgrounds. The obtained results provide explicit examples when non-abelian U-duality works well as a solution generating transformation.

36p

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Cited by in corpus (9)

• Generalized Dualities and Supergroups
• Jacobi-Lie T-plurality
• On 10 dimensional Exceptional Drinfel'd Algebras
• Towards an extended/higher correspondence -- Generalised geometry, bundle gerbes and global Double Field Theory
• Integrability structures in string theory
• Poisson-Lie T-plurality for dressing cosets
• Non-isometric U-dualities
• Extended Doubled Structures of Algebroids for Gauged Double Field Theory
• Generalised U-dual solutions in supergravity