Conjectures for Large N Superconformal N=4 Chiral Primary Four Point Functions

TL;DR

This paper proposes a general expression for four-point functions of half-BPS operators in N=4 superconformal theories at strong coupling and large N, extending previous results for specific cases.

Contribution

It introduces a unified formula for these four-point functions for any p, based on AdS integrals, and explains their structure using crossing symmetry and unitarity.

Findings

Expression matches known results for p=2,3,4

Ensures cancellation of certain long multiplet contributions

Provides a framework for understanding four-point functions at large N

Abstract

An expression for the four point function for half-BPS operators belonging to the [0,p,0] SU(4) representation in N=4 superconformal theories at strong coupling in the large N limit is suggested for any p. It is expressed in terms of the four point integrals defined by integration over AdS_5 and agrees with, and was motivated by, results for p=2,3,4 obtained via the AdS/CFT correspondence. Using crossing symmetry and unitarity, the detailed form is dictated by the requirement that at large N the contribution of long multiplets with twist less than 2p, which do not have anomalous dimensions, should cancel corresponding free field contributions.