Rings of short N=3 superfields in three dimensions and M-theory on AdS4 x N0,1,0

In this paper we investigate three-dimensional superconformal gauge theories with N = 3 supersymmetry. Independently from specific models, we derive the shortening conditions for unitary representations of the Osp(3/4) superalgebra and we express them in terms of differential constraints on three-dimensional N = 3 superfields. We find a ring structure underlying these short representations, which is just the direct generalization of the chiral ring structure of N = 2 theories. When the superconformal field theory is realized on the worldvolume of an M2-brane such a superfield ring is the counterpart of the ring defined by the algebraic geometry of the eight-dimensional 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 interaction. The AdS/CFT correspondence can be verified directly using the recently worked out Kaluza-Klein (KK) spectrum of N-0,N-1,N-0 and we find a perfect 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 corresponding 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 inspiring feature in a separate paper.