Conjectures for large N superconformal N=4 chiral primary four point functions

Abstract An expression for the four point function for 1 2 -BPS operators belonging to the [ 0 , p , 0 ] SU ( 4 ) representation in N = 4 superconformal theories at strong coupling in the large N limit is suggested for any p . It is expressed in terms of the four point integrals defined by integration over AdS 5 and agrees with, and was motivated by, results for p = 2 , 3 , 4 obtained via the AdS/CFT correspondence. It is assumed all long multiplets gain an anomalous dimension in the large N limit to leading order in 1 / N 2 . Using crossing symmetry and unitarity, the detailed form is then dictated by the requirement that at large N the contribution of long multiplets with twist less than 2 p , and which, if present in the operator product expansion for two [ 0 , p , 0 ] 1 2 -BPS operators would not have anomalous dimensions, should be absent. This requires a non-trivial cancellation with corresponding free field contributions.