AdS_5/CFT_4 Four-point Functions of Chiral Primary Operators: Cubic Vertices

TL;DR

This paper analyzes exchange diagrams in four-point functions of chiral primary operators in N=4 Super-Yang-Mills theory using AdS/CFT, identifying supergravity exchanges and computing cubic couplings to facilitate explicit calculations.

Contribution

It identifies all supergravity fields involved in exchange diagrams and computes their cubic couplings, providing tools for explicit four-point function calculations.

Findings

Computed cubic couplings for supergravity exchange fields.

Rederived normalization of quadratic action for exchanged fields.

Discussed challenges in computing complete four-point functions.

Abstract

We study the exchange diagrams in the computation of four-point functions of all chiral primary operators in D=4, $\mathcal{N}=4$ Super-Yang-Mills using AdS/CFT correspondence. We identify all supergravity fields that can be exchanged and compute the cubic couplings. As a byproduct, we also rederive the normalization of the quadratic action of the exchanged fields. The cubic couplings computed in this paper and the propagators studied extensively in the literature can be used to compute almost all the exchange diagrams explicitly. Some issues in computing the complete four-point function in the massless sector is discussed.