D=4D=4, N=2N=2 gauged supergravity coupled to vector–tensor multiplets

We construct the general four–dimensional N=2N=2 supergravity theory coupled to vector and vector–tensor multiplets only. Consistency of the construction requires the introduction of the vector fields dual to those sitting in the same supermultiplets as the antisymmetric tensors, as well as the scalar fields dual to the tensors themselves. Gauge symmetries also involving these additional fields guarantee the correct counting of the physical degrees of freedom.