Semiclassical four-point functions in AdS_5 x S^5

TL;DR

This paper develops a semiclassical approach to compute 4-point functions in AdS_5 x S^5, demonstrating consistency with known results and extending understanding of correlators involving heavy and light operators in the large charge limit.

Contribution

It introduces a factorized semiclassical method for 4-point functions with heavy and light operators, validated against known correlators and supergravity results.

Findings

Factorization of 4-point correlators into 3-point functions in the semiclassical limit

Consistency with protected extremal correlator forms in large charge limit

Matching semiclassical results with known N=4 SYM and supergravity expressions

Abstract

We consider a semiclassical (large string tension ~ \lambda^1/2) limit of 4-point correlator of two "heavy" vertex operators with large quantum numbers and two "light" operators. It can be written in a factorized form as a product of two 3-point functions, each given by the integrated "light" vertex operator on the classical string solution determined by the "heavy" operators. We check consistency of this factorization in the case of a correlator with two dilatons as "light" operators. We study in detail the example when all 4 operators are chiral primary scalars, two of which carry large charge J of order of string tension. In the large J limit this correlator is nearly extremal. Its semiclassical expression is, indeed, found to be consistent with the general protected form expected for an extremal correlator. We demonstrate explicitly that our semiclassical result matches the large J limit of the known free N=4 SYM correlator for 4 chiral primary operators with charges J,-J,2,-2; we also compare it with an existing supergravity expression. As an example of a 4-point function with two non-BPS "heavy" operators, we consider the case when the latter are representing folded spinning with large AdS spin and two "light" states being chiral primary scalars.