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 $n\leq 6$ 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$^*$-theory or Type II$^*$ 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.
Highlights
One of the most important goals when thinking of string or M-theory is to find a set of vacua, good in a certain sense
To show equivalence of the backgrounds related by a T duality transformation one singles out a set of d world-volume scalar fields corresponding to coordinates on the torus, gauges the Abelian shift symmetry Uð1Þd of the background and integrates out the Lagrange multiplier [19,20]
Most of the examples of non-Abelian U duality transformations we find are beyond the realm of the PL T duality
Summary
One of the most important goals when thinking of string or M-theory is to find a set of vacua, good in a certain sense. To show equivalence of the backgrounds related by a T duality transformation one singles out a set of d world-volume scalar fields corresponding to coordinates on the torus, gauges the Abelian shift symmetry Uð1Þd of the background and integrates out the Lagrange multiplier [19,20] Upon certain algebraic restrictions relating structure constants in the original and dual Maurer–Cartan equations, the corresponding backgrounds are equivalent from the point of view of the string This is a symmetry of the string and is usually referred to as Poisson–Lie (PL) T duality or T plurality [22,23,25] (for recent reviews see [26,27]).
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