Vacua of 5D, N=2 gauged Yang-Mills-Einstein-tensor supergravity: Abelian case - art. no. 044028

We give a detailed study of the critical points of the potentials of the si mplest nontrivial N=2 gauged Yang-Mills-Einstein supergravity theories with tensor multiplets. The scalar field target space of these examples is SO(1 ,1)xSO(2,1)/SO(2). The possible gauge groups are SO(2)xU(1)(R) and SO(1,1)x 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 manifol d. The scalar potentials of these theories consist of a contribution from t he U(1)R gauging and a contribution that is due to the presence of the tens or 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 )x U(1)R gauged theory these novel critical points correspond to anti-de Si tter ground states. For the noncompact SO(1,1)x U(1)(R) gauging, the novel ground states are de Sitter ground states. The analysis of the critical poi nts of the potential carries over in a straightforward manner to the generi c family of N = 2 gauged Yang-Mills-Einstein supergravity theories with ten sor multiplets whose scalar manifolds are of the form SO(1,1)x SO(n - 1,1)/ SO(n - 1).