Rings of short N=3 superfields in three dimensions and M-theory on AdS(4) x N-0,N-1,N-0

In this paper we investigate three-dimensional superconformal gauge theorie s with N = 3 supersymmetry. Independently from specific models, we derive t he shortening conditions for unitary representations of the Osp(3/4) supera lgebra and we express them in terms of differential constraints on three-di mensional N = 3 superfields. We find a ring structure underlying these shor t representations, which is just the direct generalization of the chiral ri ng structure of N = 2 theories. When the superconformal field theory is rea lized on the worldvolume of an M2-brane such a superfield ring is the count erpart of the ring defined by the algebraic geometry of the eight-dimension al cone transverse to the brane. This and other arguments identify the N = 3 superconformal held theory dual to M-theory compactified on AdS(4) x N-0, N-1,N-0. It is N = 3 gauge theory with SU(N) x SU(N) gauge group coupled to a suitable set of hypermultiplets, with an additional Chern-Simons interac tion. The AdS/CFT correspondence can be verified directly using the recentl y worked out Kaluza-Klein (KK) spectrum of N-0,N-1,N-0 and we find a perfec t match. We also note that besides the usual set of BPS conformal operators dual to the lightest KK states, we find that the composite operators corre sponding to certain massive KK modes are organized into a massive spin-3/2 N = 3 multiplet that might be identified with the super-Higgs multiplet of a spontaneously broken N = 4 theory. We investigate this intriguing and ins piring feature in a separate paper.