On non-abelian U-duality of 11D backgrounds

TL;DR

This paper extends non-abelian T-duality techniques to 11-dimensional supergravity backgrounds, introducing a U-duality inspired procedure that depends on the presence of spectator fields for generating solutions.

Contribution

It generalizes non-abelian T-duality to 11D backgrounds using a C-shift and U-duality, highlighting the role of spectator fields in solution generation.

Findings

Procedure can generate supergravity solutions with SL(5) algebra only with spectator fields.

The method involves a C-shift followed by U-duality or IIB section.

Restrictions on applicability are identified and discussed.

Abstract

In this letter we generalised the procedure of 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 U-duality transformation or taking a IIB section. We investigate restrictions and applicability of the procedure and find that it can provide supergravity solutions for the SL(5) exceptional Drinfeld algebra only when a spectator field is present, which is consistent with examples known in the literature.