3D superconformal theories from Sasakian seven-manifolds: new non-trivial evidences for AdS(4)/CFT3

In this paper we discuss candidate superconformal N = 2 gauge theories that realize the AdS/CFT correspondence with hi-theory compactified on the homo geneous Sasakian 7-manifolds M-7 that were classified long ago. In particul ar we focus on the two cases M-7 = Q(1,1,1) and M-7 = M-1,M-1,M-1, for the latter the Kaluza-Klein spectrum being completely known. We show how the to ric description of M-7 suggests the gauge group and the supersingleton fiel ds. The conformal dimensions of the latter can be independently calculated by comparison with the mass of baryonic operators that correspond to 5-bran es wrapped on supersymmetric 5-cycles and are charged with respect to the B etti multiplets, The entire Kaluza-Klein spectrum of short multiplets agree s with these dimensions. Furthermore, the metric cone over the Sasakian man ifold is a conifold algebraically embedded in some C-P, The ring of chiral primary fields is defined as the coordinate ring of C-p modded by the ideal generated by the embedding equations; this ideal has a nice characterizati on by means of representation theory. The entire Kaluza-Klein spectrum is e xplained in terms of these vanishing relations. We give the superfield inte rpretation of all short multiplets and we point out the existence of many l ong multiplets with rational protected dimensions, whose presence and patte rn seem to be universal in all compactifications. (C) 2000 Elsevier Science B.V. All rights reserved.