Partial spontaneous breaking of three-dimensional N=2 supersymmetry

Superfield models with 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 nonminimal self-interaction of this modified gauge superfield if we include the linear Fayet-Iliopoulos term. The dual description of the partial breaking in the model of the self-interacting Goldstone chiral superfield is also considered, These two models have constant vacuum solutions and describe the respective interactions of the N=1 Goldstone multiplets of the D2-brane and of the supermembrane with additional massive multiplets.