E11 must be a symmetry of strings and branes

We construct the dynamical equations, at low levels, that are contained in the non-linear realisation of the semi-direct product of E11E11 and its vector representation in five and eleven dimensions. Restricting these equations to contain only the usual fields of supergravity and the generalised space–time to be the usual space–time we find the equations of motion of the five and eleven dimensional maximal supergravity theories. Since this non-linear realisation contains effects that are beyond the supergravity approximation and are thought to be present in an underlying theory we conclude that the low energy effective action of string and branes should possess an E11E11 symmetry.