The Operator Product Expansion of N=4 SYM and the 4-point Functions of Supergravity

TL;DR

This paper interprets 4-point functions in N=4 SYM via AdS/CFT, revealing how supergravity calculations match OPE structures and predicting anomalous dimensions of double-trace operators in the large N limit.

Contribution

It provides a detailed OPE interpretation of supergravity-derived 4-point functions and predicts anomalous dimensions of specific double-trace operators in N=4 SYM.

Findings

Power-singular terms match OPE contributions.

Leading logarithms interpreted as 1/N^2 renormalization effects.

Predicted anomalous dimensions for double-trace operators.

Abstract

We give a detailed Operator Product Expansion interpretation of the results for conformal 4-point functions computed from supergravity through the AdS/CFT duality. We show that for an arbitrary scalar exchange in AdS(d+1) all the power-singular terms in the direct channel limit (and only these terms) exactly match the corresponding contributions to the OPE of the operator dual to the exchanged bulk field and of its conformal descendents. The leading logarithmic singularities in the 4-point functions of protected N=4 super-Yang Mills operators (computed from IIB supergravity on AdS(5) X S(5) are interpreted as O(1/N^2) renormalization effects of the double-trace products appearing in the OPE. Applied to the 4-point functions of the operators Ophi ~ tr F^2 + ... and Oc ~ tr FF~ + ..., this analysis leads to the prediction that the double-trace composites [Ophi Oc] and [Ophi Ophi - Oc Oc] have anomalous dimension -16/N^2 in the large N, large g_{YM}^2 N limit. We describe a geometric picture of the OPE in the dual gravitational theory, for both the power-singular terms and the leading logarithms. We comment on several possible extensions of our results.