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

TL;DR

This work analyzes exchange diagrams for four-point functions of all chiral primary operators in $D=4$, ${\cal N}=4$ SYM using the AdS/CFT correspondence. It identifies all Type IIB KK modes on $AdS_5\times S^5$ that can couple cubically to two external chiral primaries and derives their quadratic normalizations and complete cubic couplings among $s^I$, $t^I$, $\phi^I$, $V^I_\mu$, $W^I_\mu$, and $H^I_{(\mu\nu)}$, expressed via KK overlaps in Appendix A. The analysis confirms consistency with the massless multiplet and the gauged supergravity truncation, reproducing the expected current and stress-tensor couplings with a fixed gauge coupling $g^2=4$, and provides a practical framework to compute exchange diagrams using known propagators. Overall, the results furnish a comprehensive set of cubic vertices enabling explicit evaluation of most exchange contributions to four-point functions and facilitating strong-weak coupling comparisons in SYM$_4$.

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.

Figures (1)

• Figure 1: The two types of supergravity diagram contributing to the AdS computation of four-point functions of chiral primary operators..