U-duality covariant gravity

Understand

We extend the techniques of double field theory to more general gravity theories and U-duality symmetries, having in mind applications to the complete D=11 supergravity.

• In this paper we work out a (3+3)-dimensional `U-duality covariantization' of D=4 Einstein gravity, in which the Ehlers group SL(2,R) is realized geometrically, acting in the 3 representation on half of the coordinates.
• We include the full (2+1)-dimensional metric, while the `internal vielbein' is a coset representative of SL(2,R)/SO(2) and transforms under gauge transformations via generalized Lie derivatives.
• In addition, we introduce a gauge connection of the `C-bracket', and a gauge connection of SL(2,R), albeit subject to constraints.