We construct the classical action of the Aharony-Bergman-Jafferis-Maldacena (ABJM) model in the N =3, d=3 harmonic superspace. In such a formulation three out of six supersymmetries are realized off shell while the other three mix the superfields and close on shell. The superfield action involves two hypermultiplet superfields in the bifundamental representation of the gauge group and two Chern-Simons gauge superfields corresponding to the left and right gauge groups. The N =3 superconformal invariance allows only for a minimal gauge interaction of the hypermultiplets. Amazingly, the correct sextic scalar potential of ABJM emerges after the elimination of auxiliary fields. Besides the original U(N ) × U(N ) ABJM model, we also construct N =3 superfield formulations of some generalizations. For the SU(2) × SU(2) case we give a simple superfield proof of its enhanced N =8 supersymmetry and SO(8) R-symmetry.
The N = 1 supergravity in superspace (more precisely the minimal Einstein version of it) is consistently reformulated as a simultaneous nonlinear realization of two complex finite-dimensional supergroups generating via their closure the whole infinite-dimensional N = 1 supergravity group and having in their intersection the rigid N = 1 Poincare supergroup chosen as the vacuum-stability subgroup. Thus N = 1 supergravity is found to be a kind of nonlinear a model describing a partial spontaneous breaking of the infinite-dimensional supersymmetry down to the rigid N = 1 supersymmetry. The only independent Goldstone superfield accompanying this breaking appears to be an axial-vector superfield Hpb (x,8,8) identified with the N = 1 supergravity prepotential. All the other Goldstone superfields are expressed in terms of H p p by imposing appropriate covariant constraints on the corresponding Cartan superforms (the inverse Higgs effect). Thereby, the 15-year-old result of Borisov and Ogievetsky who interpreted Einstein gravity as a nonlinear a model is generalized to the N = 1 supergravity case. Possible implications of the proposed formulation are discussed. In particular, the intriguing analogy between N = 1 supergravity and the (super) p-brane theories is pointed out.
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