Operator product expansion of the lowest weight CPOs in N=4 SYM4 at strongcoupling

We present a detailed analysis of the 4-point functions of the lowest weigh t chiral primary operators O-I similar to tr(phi((i)phi(j))) in N= 4 SYM4 a t strong coupling and show that their structure is compatible with the pred ictions of AdS/CFT correspondence. In particular, all power-singular terms in the 4-point functions exactly coincide with the contributions coming fro m the conformal blocks of the CPOs, the R-symmetry current and the stress t ensor. Operators dual to string modes decouple at strong coupling. We compu te the anomalous dimensions and the leading 1/N-2 corrections to the normal ization constants of the 2- and 3-point functions of scalar and vector doub le-trace operators with approximate dimensions 4 and 5, respectively. We al so find that the conformal dimensions of certain towers of double-trace ope rators in the 105, 84 and 175 irreps are non-renormalized. We show that, de spite the absence of a non-renormalization theorem for the double-trace ope rator in the 20 irrep, its anomalous dimension vanishes. As by-products of our investigation, we derive explicit expressions for the conformal block o f the stress tensor, and for the conformal partial wave amplitudes of a con served current and of a stress tensor in d dimensions. (C) 2000 Elsevier Sc ience B.V. All rights reserved.