The E11 origin of all maximal supergravities

Starting from the eleven dimensional E₁₁ non-linear realisation of M-theory we compute all possible forms, that is objects with totally antisymmetrised indices, that occur in four dimensions and above as well as all the 1-forms and 2-forms in three dimensions. In any dimension D, the D-1-forms lead to maximal supergravity theories with cosmological constants and they are in precise agreement with the patterns of gauging found in any dimension using supersymmetry. The D-forms correspond to the presence of space-filling branes which are crucial for the consistency of orientifold models and have not been derived from an alternative approach, with the exception of the 10-dimensional case. It follows that the gaugings of supergravities and the spacetime-filling branes possess an eleven dimensional origin within the E₁₁ formulation of M-theory. This and previous results very strongly suggest that all the fields in the adjoint representation of E₁₁ have a physical interpretation.