Low Energy Processes Associated with Spontaneously Broken N=2 Supersymmetry

We consider low energy processes described by the N=2 supercurrent on its partially (to N=1) and spontaneously broken vacuum and the attendant Nambu-Goldstone fermion (NGF), which the presence of the electric and magnetic Fayet-Iliopoulos (FI) terms is responsible for. We show suppressions of amplitudes decaying into the NGF as its momentum becomes small. In the lagrangian realization (namely, the model of arXiv:hep-th/0409060) of the conserved supercurrent, the NGF resides in the overall U(1), which is nonetheless not decoupled, and interacts with the SU(N) sector through nonderivative as well as derivative couplings. The low energy suppression is instead accomplished by a cancellation between the annihilation diagram from the Yukawa couplings and the contact four-Fermi terms. We give a complete form of the supercurrent and the model is recast in more transparent notation.