Vacua of 5D, [formula presented] gauged Yang-Mills-Einstein-tensor supergravity: Abelian case

We give a detailed study of the critical points of the potentials of the simplest nontrivial (Formula presented) gauged Yang-Mills-Einstein supergravity theories with tensor multiplets. The scalar field target space of these examples is (Formula presented) The possible gauge groups are (Formula presented) and (Formula presented) where (Formula presented) is a subgroup of the R-symmetry group (Formula presented) and (Formula presented) and (Formula presented) are subgroups of the isometry group of the scalar manifold. The scalar potentials of these theories consist of a contribution from the (Formula presented) gauging and a contribution that is due to the presence of the tensor fields. We find that the latter contribution can change the form of the supersymmetric extrema from maxima to saddle points. In addition, it leads to novel critical points not present in the corresponding gauged Yang-Mills-Einstein supergravity theories without the tensor multiplets. For the (Formula presented) gauged theory these novel critical points correspond to anti–de Sitter ground states. For the noncompact (Formula presented) gauging, the novel ground states are de Sitter ground states. The analysis of the critical points of the potential carries over in a straightforward manner to the generic family of (Formula presented) gauged Yang-Mills-Einstein supergravity theories with tensor multiplets whose scalar manifolds are of the form (Formula presented).