Abstract
Recently a Mellin-space formula was conjectured for the form of correlation functions of 1/2 BPS operators in planar mathcal{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.
Highlights
The problem of finding holographic four-point correlation functions in this particular limit has gained renewed interest
The existence of the simple Mellin-space formula is surprising when one considers the only method known at present to explicitly compute these correlation functions: one considers the tree-level Witten diagrams for the chosen operators, whose vertices follow from the effective action of the Kaluza-Klein reduction of the type IIB supergravity on S5 [9,10,11]
As of yet all the explicitly computed four-point functions are in some form not completely generic: the first computed correlators were the equal-weight ones for 1/2 BPS operators with weight k = 2 [12, 13], k = 3 [14] and k = 4 [15], where the computation gets simplified due to the internal symmetry
Summary
This time the partitions b form a symmetric 4 × 4-matrix with zeroes on the diagonal, but they satisfy the modified equations bij = ki − 2 This reduces the number of partitions b significantly, implying that the correlator can be written as a sum over only a few independent functions Fb of u and v, which are conformally invariant by construction and carry all the dependence on the ’t Hooft coupling. We will use this decomposition of the correlator for two purposes: firstly to be able to present our computed correlators in a compact form {Fb}. We will discuss how one can compute these two parts for a concrete set of weights separately, beginning with the latter
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