BMN Correlators and Operator Mixing in N=4 Super Yang-Mills Theory

TL;DR

This paper investigates correlation functions and operator mixing in N=4 Super Yang-Mills theory within the BMN limit, revealing issues with four-point functions, refining non-planar corrections, and constructing corrected operators with consistent anomalous dimensions.

Contribution

It provides a full resolution to the genus one operator mixing problem and constructs the correct operators with their anomalous dimensions in the BMN limit.

Findings

Non-extremal four-point functions are ill-defined in the BMN limit.

A full resolution to the genus one operator mixing problem is presented.

All three types of operators share the same torus anomalous dimension.

Abstract

Correlation functions in perturbative N=4 supersymmetric Yang-Mills theory are examined in the Berenstein-Maldacena-Nastase (BMN) limit. We demonstrate that non-extremal four-point functions of chiral primary fields are ill-defined in that limit. This lends support to the assertion that only gauge theoretic two-point functions should be compared to pp-wave strings. We further refine the analysis of the recently discovered non-planar corrections to the planar BMN limit. In particular, a full resolution to the genus one operator mixing problem is presented, leading to modifications in the map between BMN operators and string states. We give a perturbative construction of the correct operators and we identify their anomalous dimensions. We also distinguish symmetric, antisymmetric and singlet operators and find, interestingly, the same torus anomalous dimension for all three. Finally, it is discussed how operator mixing effects modify three point functions at the classical level and, at one loop, allow us to recover conformal invariance.