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

In this paper we fill a necessary gap in order to realize an explicit comparison between the Kaluza-Klein spectra of supergravity compactified on AdS4× X 7and superconformal field theories living on the worldvolume of M2-branes. On the algebraic side we consider the superalgebra Osp ( | 4) and we study the double interpretation of its unitary irreducible representations either as supermultiplets of particle states in the bulk or as a conformal superfield on the boundary. On the Lagrangian field theory side we construct, using rheonomy rather than superfield techniques, the generic form of an = 2, d= 3 gauge theory. Indeed, the superconformal multiplets are supposed to be composite operators in a suitable gauge theory