Four-point functions of all-different-weight chiral primary operators in the supergravity approximation

Abstract

Abstract Recently a Mellin-space formula was conjectured for the form of correlation functions of 1/2 BPS operators in planar $$ \mathcal{N}=4 $$ N = 4 SYM in the strong ’t Hooft coupling limit. In this work we report on the computation of two previously unknown four-point functions of operators with weights 〈2345〉 and 〈3456〉, from the effective type-IIB supergravity action using AdS/CFT. These correlators are novel: they are the first correlators with all different weights and in particular 〈3456〉 is the first next-next-next-to-extremal correlator to ever have been computed. We also present simplifications of the known algorithm, without which these computations could not have been executed. These simplifications consist of a direct formula for the exchange part and for the contact part of the correlation function, as well as a simplification of the C tensor algorithm to compute a tensors. After bringing our results in the appropriate form we successfully corroborate the recently conjectured formula.