Osp(N|4) supermultiplets as conformal superfields on partial AdS₄ and the generic form of N=2, D=3 gauge theories

In this paper we fill a necessary gap in order to realize the explicit comparison between the Kaluza Klein spectra of supergravity compactified on AdS_4 x X^7 and superconformal field theories living on the world volume of M2-branes. On the algebraic side we consider the superalgebra Osp(N|4) and we study the double interpretation of its irreducible representations either as supermultiplets of particle states in the bulk or as conformal superfields on the boundary. On the lagrangian field theory side we construct, using rheonomy rather than superfield techniques, the generic form of an N=2, d=3 gauge theory. Indeed the superconformal multiplets are supposed to be composite operators in a suitable gauge theory.