Operator Product Expansion of the Lowest Weight CPOs in N=4 SYM_4 at Strong Coupling

Abstract

We present a detailed analysis of the 4-point functions of the lowest weight chiral primary operators $O^{I} \sim \tr \phi^{(i}\phi^{j)}$ in $\N =4$ SYM$_4$ at strong coupling and show that their structure is compatible with the predictions of AdS/CFT correspondence. In particular, all power-singular terms in the 4-point functions exactly coincide with the contributions coming from the conformal blocks of the CPOs, the R-symmetry current and the stress tensor. Operators dual to string modes decouple at strong coupling. We compute the anomalous dimensions and the leading $1/N^2$ corrections to the normalization constants of the 2- and 3-point functions of scalar and vector double-trace operators with approximate dimensions 4 and 5 respectively. We also find that the conformal dimensions of certain towers of double-trace operators in the {\bf 105}, {\bf 84} and {\bf 175} irreps are non-renormalized. We show that, despite the absence of a non-renormalization theorem for the double-trace operator in the {\bf 20} irrep, its anomalous dimension vanishes. As by-products of our investigation, we derive explicit expressions for the conformal block of the stress tensor, and for the conformal partial wave amplitudes of a conserved current and of a stress tensor in $d$ dimensions.