Duality Invariant Actions and Generalised Geometry
  We construct the non-linear realisation of the semi-direct product of E(11) and its first fundamental representation at lowest order and appropriate to spacetime dimensions four to seven. This leads to a non-linear realisation of the duality groups and introduces fields that depend on a generalised space which possess a generalised vielbein. We focus on the part of the generalised space on which the duality groups alone act and construct an invariant action. 
David S. Berman, Hadi Godazgar, Malcolm J. Perry, Peter West
hep-th