Partial spontaneous breakdown of 3-dimensional N=2 supersymmetry

The superfield models with the partial spontaneous breaking of the global D=3, N=2 supersymmetry are discussed. The abelian gauge model describes low-energy interactions of the real scalar field with the 3D vector and fermion fields. We introduce the new Goldstone-Maxwell representation of the 3D gauge superfield and show that the partial spontaneous breaking N=2 → N=1 is possible for the non-minimal self-interaction of this modified gauge superfield including the linear Fayet-Iliopoulos term. The dual description of the partial breaking in the model of self-interacting Goldstone chiral superfield is also considered. These models have the constant vacuum solutions and describe, respectively, the interactions of the N=1 Goldstone multiplets of the D2-brane or supermembrane with the additional massive multiplets