Matter coupling and non-linear σ-models in N = 2 supergravity

Starting from an off-shell formulation of N = 2 supergravity, we construct the matter multiplet in its complex form (the scalar hypermultiplet) and in its real form. We construct the matter action which describes the coupling to supergravity. The interpretation where the 32 + 32 field components of the minimal gravitational multiplet are independent dynamical variables is known to be inconsistent for pure supergravity. We find it to be consistent when coupled to at least one matter multiplet, and to give rise to supersymmetric σ-models when coupled to at least two matter multiplets.