Correlation Functions and Massive Kaluza-Klein Modes in the AdS/CFT Correspondence

TL;DR

This paper analyzes four-point correlation functions of BPS operators in N=4 SYM, revealing partial non-renormalisation, and computes supergravity amplitudes that match field theory predictions, highlighting the structure of massive Kaluza-Klein modes.

Contribution

It demonstrates partial non-renormalisation of four-point functions for certain BPS operators and computes supergravity amplitudes that align with field theory expectations, revealing a simple sigma-model structure.

Findings

Four-point functions are partially non-renormalised and determined by a limited number of functions.

Supergravity calculations match the predicted structure of correlators, splitting into free and interacting parts.

The effective Lagrangian for the relevant KK modes has a simple sigma-model form.

Abstract

We study four-point correlation functions of 1/2-BPS operators in N=4 SYM which are dual to massive KK modes in AdS_5 supergravity. On the field theory side, the procedure of inserting the SYM action yields partial non-renormalisation of the four-point amplitude for such operators. In particular, if the BPS operators have dimensions equal to three or four, the corresponding four-point amplitude is determined by one or two independent functions of the two conformal cross-ratios, respectively. This restriction on the amplitude does not merely follow from the superconformal Ward identities, it also encodes dynamical information related to the structure of the gauge theory Lagrangian. The dimension 3 BPS operator is the AdS/CFT dual of the first non-trivial massive Kaluza-Klein mode of the compactified type IIB supergravity, whose interactions go beyond the level of the five-dimensional gauged N=8 supergravity. We show that the corresponding effective Lagrangian has a surprisingly simple sigma-model-type form with at most two derivatives. We then compute the supergravity-induced four-point amplitude for the dimension 3 operators. Remarkably, this amplitude splits into a "free" and an "interacting" parts in exact agreement with the structure predicted by the insertion procedure. The underlying OPE fulfills the requirements of superconformal symmetry and unitarity.