E11-extended spacetime and gauged supergravities

We formulate all the five dimensional gauged maximal supergravity theories as non-linear realisations of the semi-direct product of E11 and a set of generators which transform according to the first fundamental representation l of E11. The latter introduces a generalised space-time which plays a crucial role for these theories. We derive the E11 and l transformations of all the form fields and their dynamics. We also formulate the five dimensional gauged supergravity theories using the closure of the supersymmetry algebra. We show that this closes on the bosonic field content predicted by E11 and we derive the field transformations and the dynamics of this theory. The results are in precise agreement with those found from the E11 formulation. This provides a very detailed check of E11 and also the first substantial evidence for the generalised space-time. The results can be generalised to all gauged maximal supergravities, thus providing a unified framework of all these theories as part of E11