Searching for all N=4 supergravities with global SO(4)

A more compact superspace formulation for the ungauged N=4 supergravity theories without auxiliary fields is given. Superspace geometry is used to search for all N=4 supergravities with at least SO(4) global symmetry. We find that the general solutions to the unconstrained Bianchi identities, with the field content of N=4 supergravity, are equivalent to the known SO(4) and SU(4) supergravities up to field redefinitions. Therefore, the N=4 supergravities follow uniquely from their known field representations and the Bianchi identities with no further constraints. (orig.)