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

TL;DR

This work analyzes the four-point functions of the lowest weight chiral primary operators in N=4 SYM_4 at strong coupling using AdS/CFT, showing that the leading singular terms reproduce the conformal blocks of the CPO, the R-symmetry current, and the stress tensor, while string-mode exchanges decouple. It computes anomalous dimensions and leading 1/N^2 corrections to the normalization constants of certain double-trace operators, finding non-renormalization for several SO(6) irreps and a negative anomalous dimension for the singlet scalar, consistent with operator-descendant relations. The results reveal a consistent pattern of operator splitting: free-field double-trace operators decompose into supergravity-coupled and string-mode sectors, with only the former surviving at strong coupling; many tensor towers exhibit protected dimensions, while normalization constants can still receive strong-coupling corrections. The paper also provides explicit conformal blocks and CPWAs for conserved currents and the stress tensor, along with detailed projector techniques for SO(6) representations, enabling broader applications to AdS/CFT and CFT OPE analyses.

Abstract

We present a detailed analysis of the 4-point functions of the lowest weight chiral primary operators $O^{I} \sim \tr φ^{(i}φ^{j)}$ 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.