We develop new techniques to compute five-point correlation functions from IIB supergravity on AdS 5 × S 5. Our methods rely entirely on symmetry and general consistency conditions, and eschew detailed knowledge of the supergravity effective action. We demonstrate our methods by computing the five-point function of the 20 operator, which is the superconformal primary of the stress tensor multiplet. We also develop systematic methods to compute the five-point conformal blocks in series expansions. Using the explicit expressions of the conformal blocks, we perform a Euclidean OPE analysis of the 20 five-point function. We find expected agreement with non-renormalized quantities and also extract new CFT data at strong coupling.

The four-point function of length-two half-BPS operators in N = 4 SYM receives nonplanar corrections starting at four loops. Previous work relied on the analysis of symmetries and logarithmic divergences to fix the integrand up to four constants. In this work, we compute those undetermined coefficients and fix the integrand completely by using the reformulation of N = 4 SYM in twistor space. The final integrand can be written as a combination of finite conformal integrals and we have used the method of asymptotic expansions to extract non-planar anomalous dimensions and structure constants for twist-two operators up to spin eight. Some of the results were already know in the literature and we have found agreement with them.

This paper has two parts. We first compute the leading contribution to the strong-coupling mixing between the Konishi operator and a double-trace operator composed of chiral primaries by using flat-space vertex operators for the string-duals of the operators. We then compute the three-point functions for protected or unprotected scalar operators with higher spin operators on the leading Regge trajectory. Here we see that the nontrivial spatial structures required by conformal invariance arise naturally from the form of the polarization tensors in the vertex operators. We find agreement with recent results extracted from Mellin amplitudes for four-point functions, as well as with earlier supergravity calculations. We also obtain some new results for other combinations of operators.

Abstract:We compute the three-point structure constants for short primary operators of N = 4 super Yang-Mills theory to leading order in 1/ √ λ by mapping the problem to a flat-space string theory calculation. We check the validity of our procedure by comparing to known results for three chiral primaries. We then compute the three-point functions for any combination of chiral and non-chiral primaries, with the non-chiral primaries all dual to string states at the first massive level. Along the way we find many cancellations that leave us with simple expressions, suggesting that integrability is playing an important role.

We obtain all planar four-point correlators of half-BPS operators in N = 4 SYM up to five loops. The ansatz for the integrand is fixed partially by imposing lightcone OPE relations between different correlators. We then fix the integrated correlators by comparing their asymptotic expansions with simple data obtained from integrability. We extract OPE coefficients and find a prediction for the triple wrapping correction of the hexagon form factors, which contributes already at the five-loop order.