Next-next-to-extremal Four Point Functions of N=4 1/2 BPS Operators in the AdS/CFT Correspondence

TL;DR

This paper analyzes four-point functions of N=4 1/2 BPS operators at strong coupling and large N, confirming supergravity predictions and their consistency with superconformal symmetry and free field theory results.

Contribution

It introduces new techniques to evaluate supergravity couplings and demonstrates the splitting of four-point amplitudes into free and interactive parts consistent with conjectured structures.

Findings

Four derivative couplings vanish on-shell in supergravity.

Four point amplitude splits into free and interactive parts.

Results support the superconformal symmetry and conjectures about correlator structures.

Abstract

Four point functions of general N=4 1/2-BPS primary fields, satisfying the next-next-to-extremality condition \Delta_{1}+\Delta_{2}+\Delta_{3}-\Delta_{4}=4 are studied at large N and strong coupling. We apply new techniques to evaluate the effective couplings in supergravity, and confirm that the four derivative couplings arising in the five-dimensional supergravity vanish on-shell. We then show that the four point amplitude resulting from supergravity naturally splits into a "free" and an interactive part which resembles an effective quartic interaction. The precise structure agrees with superconformal symmetry and supports the conjecture formulated by Dolan, Osborn and Nirschl regarding the strongly coupled form of four point correlators of chiral primary operators. We also evaluate the amplitude in large N free field SYM theory and discuss the results in the context of the correspondence.