The operator product expansion of N=4 SYM and the 4-point functions of supergravity

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 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 AdS₅×S⁵) are interpreted as O(1/N²) renormalization effects of the double-trace products appearing in the OPE. Applied to the 4-point functions of the operators O_φ~(trF²+) and O_C~(trFF̃+), this analysis leads to the prediction that the double-trace composites [O_φO_C] and [O_φO_φ-O_CO_C] have anomalous dimension -16/N² in the large N, large g_YM²N 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.