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

Abstract

Four point functions of general N=4 1/2-BPS primary fields, satisfying the next-next-to-extremality condition Δ_{1}+Δ_{2}+Δ_{3}-Δ_{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.

40 pages, 6 figures, 6 appendices. Minor corrections

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