Vacua of 5D, N=2 gauged Yang-Mills-Einstein-tensor supergravity: Abelian case

We give a detailed study of the critical points of the potentials of the simplest nontrivial N=2 gauged Yang-Mills-Einstein supergravity theories with tensor multiplets. The scalar field target space of these examples is SO(1,1)×SO(2,1)/SO(2). The possible gauge groups are SO(2)×U(1)_R and SO(1,1)×U(1)_R, where U(1)_R is a subgroup of the R-symmetry group SU(2)_R, and SO(2) and SO(1,1) are subgroups of the isometry group of the scalar manifold. The scalar potentials of these theories consist of a contribution from the U(1)_R 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 SO(2)×U(1)_R gauged theory these novel critical points correspond to anti-de Sitter ground states. For the noncompact SO(1,1)×U(1)_R 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 N=2 gauged Yang-Mills-Einstein supergravity theories with tensor multiplets whose scalar manifolds are of the form SO(1,1)×SO(n-1,1)/SO(n-1).