Matter coupling in N = 4 supergravity

An arbitrary number of abelian vector multiplets is coupled to N = 4 supergravity. The resulting action is invariant under global SO(n,6), where n is the number of vector multiplets, and under local SU(4) × U(1) transformations. The scalar fields of the theory parametrize the manifold [SO(n,6)/SO(n) × SO(6)] × [SU(1,1)/U(1)]. The role of the matter fields of the N = 4 Weyl multiplet in the Poincaré supergravity theory is clarified.