On Feynman rules for Mellin amplitudes in AdS/CFT

The computation of CFT correlation functions via Witten diagrams in AdS space can be simplified via the Mellin transform. Recently a set of Feynman rules for tree-level Mellin space amplitudes has been proposed for scalar theories. In this note we derive these rules by explicitly evaluating all of the relevant Witten diagram integrals for the scalar phi^n theory. We also check that the rules reduce to the usual Feynman rules in the flat space limit.Comment: minor corrections, published versio

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

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.Comment: 40 pages, 6 figures, 6 appendices. Minor correction

Flavour singlets in gauge theory as permutations

50 pages, v2: typos corrected, v3: to appear in JHEPJHEP is an open-access journal funded by SCOAP3 and licensed under CC BY 4.