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-Kähler manifold is gauged together with a SU(2) R-symmetry subgroup. We construct several solutions of the CP‾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‾3 model, we construct an AdS2×S2 solution which is only 1/8 BPS and an R×H3 solutions that also preserves 1 of the 8 possible supersymmetries. We show how to use dimensional reduction as in the ungauged case to obtain Rn×Sm and also AdSn×Sm-type solutions (with different radii) in 5- and 4-dimensions from the 6-dimensional AdS3×S3 solution.