A General Study of Ground States of N=2 Supergravity Theories with   Symmetric Scalar Manifolds in 5 Dimensions
  After reviewing the existing results we give an extensive analysis of the critical points of the potentials of the gauged N=2 Yang-Mills/Einstein Supergravity theories coupled to tensor- and hyper multiplets. Our analysis includes all the possible gaugings of all N=2 Maxwell-Einstein supergravity theories whose scalar manifolds are symmetric spaces. In general, the scalar potential gets contributions from R-symmetry gauging, tensor couplings and hyper-couplings. We show that the coupling of a hypermultiplet into a theory whose potential has a non-zero value at its critical point, and gauging a compact subgroup of the hyperscalar isometry group will only rescale the value of the potential at the critical point by a positive factor, and therefore will not change the nature of an existing critical point. However this is not the case for non-compact SO(1,1) gaugings. An SO(1,1) gauging of the hyper isometry will generally lead to deSitter vacua, which is analogous to the ground states found by simultaneously gauging SO(1,1) symmetry of the real scalar manifold with U(1)_R in earlier literature. SO(m,1) gaugings with m>1, which give contributions to the scalar potential only in the Magical Jordan family theories, on the other hand, do not lead to deSitter vacua. Anti-deSitter vacua are generically obtained when the U(1)_R symmetry is gauged. We also show that it is possible to embed certain generic Jordan family theories into the Magical Jordan family preserving the nature of the ground states. However the Magical Jordan family theories have additional ground states which are not found in the generic Jordan family theories. 
O. Ogetbil