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 CP3 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 CP3 model, we construct an AdS2xS2 solution which is only 1/8 BPS and an RxH3 solution that also preserves 1 of the 8 possible supersymmetries. We show how to use dimensional reduction as in the ungauged case to obtain RnxSm and also AdSnxSm-type solutions (with different radii) in - and 4 dimensions from the 6-dimensional AdS3xS3 solution.