Modified N = 2 supersymmetry and Fayet-Iliopoulos terms

Peculiarities of realization of N = 2 supersymmetry in N = 2 abelian gauge theory with two sorts of Fayet-Iliopoulos terms, electric and magnetic ones, within manifestly supersymmetric formulations via the Mezincescu and harmonic-analytic prepotential are studied. A magnetic, duality-transformed superfield form of the N = 2 Maxwell effective holomorphic action with standard electric Fayet-Iliopoulos term and demonstrate that in such a system off-shell N = 2 supersymmetry is inevitably realized in an unusual Goldstone mode corresponding to the partial spontaneous breaking down to N = 1 is found. On shell, the standard total breaking occurs. In a system with the two sorts of Fayet-Iliopoulos terms, off-shell N = 2 supersymmetry is realized in the partial breaking mode, both in the electric and magnetic representations. This regime is retained on shell due to the Antoniadis-Partouche-Taylor mechanism. It is shown that the off-shell algebra of N = 2 supersymmetry in the partial breaking realization is modified on gauge-variant objects like potentials and prepotentials. The closure of spinor charges involves some special gauge transformations before any gauge fixing