Note on S-channel factorization in multitrace Berenstein-Maldacena-Nastase correlators

TL;DR

This paper addresses a puzzle in the factorization of BMN correlators in free super-Yang-Mills theory, resolving it by including previously missed diagrams and supporting their interpretation as string loop amplitudes.

Contribution

The paper resolves a specific breakdown in S-channel factorization by identifying missing diagrams, strengthening the link between correlators and string loop amplitudes.

Findings

Resolved the S-channel factorization puzzle

Identified diagrams previously overlooked

Supported the interpretation of higher genus correlators as string loops

Abstract

In a previous paper we proposed a factorization principle for the correlation functions of Berenstein-Maldacena-Nastase (BMN) operators in free $\mathcal{N}=4$ super-Yang-Mills theory. These correlators are conjectured to described physical string amplitudes in an infinitely curved Ramond-Ramond pp-wave background. There was a puzzle that the factorization seems to break down for $S$-channel in the $2\rightarrow 2$ scattering process. Here we resolve this puzzle by including some diagrams missed in the previous paper. We also observe some interesting relations which further support the interpretation of higher genus correlators as physical string loop amplitudes.