On the Non-Abelian U-Duality of 11D Backgrounds

Abstract

In this work, we generalise the procedure of the non-abelian T-duality based on a B-shift and a sequence of formal abelian T-dualities in non-isometric directions to 11-dimensional backgrounds. This consists of a C-shift followed by either a formal (abelian) U-duality transformation or taking an IIB section. By construction, this is a solution generating transformation. We investigate the restrictions and applicability of the procedure and find that it can provide supergravity solutions for the SL(5) exceptional Drinfeld algebra only when the isometry algebra of the sigma-model target space decomposes into a direct sum. This is consistent with examples known in the literature.