Gauged matter coupling in N = 4 supergravity

Gauged N = 4 supergravity with an arbitrary number of matter multiplets is constructed from a superconformal starting point. It includes both the SO(4) and SU(4) symmetric N = 4 supergravity theories, and all their gaugings. Noncompact Yang-Mills symmetries may mix the matter and supergravity vector fields. We establish that in matter coupled N = 4 supergravity theories the super-Higgs effect can occur with a vanishing cosmological constant. An example is given with gauged SO(3) × SO(2, 1) symmetry in which the scalar potential vanishes completely, and all four supersymmetries are broken.