Partial breaking of N=2 supersymmetry and decoupling limit of Nambu-Goldstone fermion in U(N) gauge model

We study the N=1 U(N) gauge model obtained by spontaneous breaking of N=2 supersymmetry. The Fayet-Iliopoulos term included in the N=2 action does not appear in the resulting N=1 action and the superpotential is modified to break discrete R symmetry. We take a limit in which the Kähler metric becomes flat and the superpotential preserves non-trivial form. The Nambu-Goldstone fermion is decoupled from other fields but the resulting action is still N=1 supersymmetric. It shows the origin of the fermionic shift symmetry in N=1 U(N) gauge theory.