Partial supersymmetry breaking and N=2 U(Nc) gauge model with hypermultiplets in harmonic superspace

We provide a manifestly N=2 supersymmetric formulation of the N=2 U(Nc) gauge model constructed in terms of N=1 superfields in hep-th/0409060. The model is composed of N=2 vector multiplets in harmonic superspace and can be viewed as the N=2 U(Nc) Yang-Mills effective action equipped with the electric and magnetic Fayet-Iliopoulos terms. We generalize this gauge model to an N=2 U(Nc) QCD model by introducing N=2 hypermultiplets in harmonic superspace which include both the fundamental representation of U(Nc) and the adjoint representation of U(Nc). The effect of the magnetic Fayet-Iliopoulos term is to shift the auxiliary field by an imaginary constant. Examining vacua of the model, we show that N=2 supersymmetry is spontaneously broken down to N=1.