Supersymmetric solutions of SU(2)-Fayet-Iliopoulos-gauged N=2, d=4 supergravity

We explore the construction of supersymmetric solutions of theories of N = 2, d = 4 supergravity with a SU(2) gauging and SU(2) Fayet-Iliopoulos terms. In these theories an SU(2) isometry subgroup of the Special-Kahler manifold is gauged together with a SU(2) R-symmetry subgroup. We construct several solutions of the (CP) over bar (3) quadratic model directly in four dimensions and of the ST[2, 6] model by dimensional reduction of the solutions found by Cariglia and Mac Conamhna in N = (1, 0), d = 6 supergravity with the same kind of gauging. In the (CP) over bar (3) model, we construct an AdS(2) x S-2 solution which is only 1/8 BPS and an R x H-3 solutions that also preserves 1 of the 8 possible supersymmetries. We show how to use dimensional reduction as in the ungauged case to obtain R-n x S-m and also AdS(n) x S-m-type solutions (with different radii) in 5- and 4-dimensions from the 6-dimensional AdS(3) x S-3 solution.