Osp(N vertical bar 4) supermultiplets as conformal superfields on partial derivative AdS(4) 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 compa rison between the Kaluza-Klein spectra of supergravity compactified on AdS( 4) x X-7 and superconformal field theories living on the worldvolume of M2- branes. On the algebraic side we consider the superalgebra Osp(N/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 construc t, using rheonomy rather than superfield techniques, the generic form of an N = 2, d = 3 gauge theory. Indeed, the superconformal multiplets are suppo sed to be composite operators in a suitable gauge theory.