Veneziano Amplitude of Vasiliev Theory

TL;DR

This paper calculates four-point functions in CFTs with weakly broken higher spin symmetry, revealing the analytic structure of OPE data in spin and connecting to Vasiliev theory via the Veneziano amplitude.

Contribution

It provides a detailed computation of four-point functions in higher spin symmetric CFTs and clarifies the analytic properties of OPE data, linking to Vasiliev theory and AdS/CFT correspondence.

Findings

OPE data is analytic in spin for J ≥ 1.

Contact Witten diagrams contribute non-analytic terms in spin.

Large N Chern-Simons matter theories lack these non-analytic contact terms.

Abstract

We compute the four-point function of scalar operators in CFTs with weakly broken higher spin symmetry at arbitrary 't Hooft coupling. We use the known three-point functions in these theories, the Lorentzian OPE inversion formula and crossing to fix the result up to the addition of three functions of the cross ratios. These are given by contact Witten diagrams in AdS and manifest non-analyticity of the OPE data in spin. We use Schwinger-Dyson equations to show that such terms are absent in the large $N$ Chern-Simons matter theories. The result is that the OPE data is analytic in spin up to $J=0$.