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 $N=2\to N=1$ 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.