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, En(n) EDA with n≤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 generalized 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.