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We explore the construction of supersymmetric solutions of theories ofN=2,d=4 supergravity with a SU(2) gauging and SU(2) Fayet-Iliopoulos terms. Inthese theories an SU(2) isometry subgroup of the Special Kahler manifold isgauged together with a SU(2) R-symmetry subgroup. We construct severalsolutions of the CP3 quadratic model directly in four dimensions and of theST[2,6] model by dimensional reduction of the solutions found by Cariglia andMac Conamhna in N=(1,0),d=6 supergravity with the same kind of gauging. In theCP3 model, we construct an AdS2xS2 solution which is only 1/8 BPS and an RxH3solution that also preserves 1 of the 8 possible supersymmetries. We show howto use dimensional reduction as in the ungauged case to obtain RnxSm and alsoAdSnxSm-type solutions (with different radii) in - and 4 dimensions from the6-dimensional AdS3xS3 solution.

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