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 OI ~ tr?(i?j) in N = 4 SYM4 at strong coupling and show that their structure is compatible with the predictions of AdS/CFT correspondence. In particular, all powersingular 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/N2 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 105, 84 and 175 irreps are non-renormalized. We show that, despite the absence of a non-renormalization theorem for the double-trace operator in the 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.