Yang-Mills theories coupled to n = 2 supergravity

All stationary points of the scalar potential of pure Yang-Mills theories minimally coupled to n = 2 gauged supergravity are found. For arbitrary Yang-Mills groups G, the supersymmetry-preserving extremum does not break G. All other stationary points break both the Yang-Mills group and n = 2 supersymmetry in anti de Sitter space. For G = SU(N), we explicitly construct locally stable solutions with maximal residual symmetry as well as solutions with unbroken SU(3) x SU(2) x U(1). (orig.)