BMN Operators and Superconformal Symmetry

TL;DR

This paper explores how N=4 superconformal symmetry constrains BMN operators with two charge defects, revealing they form a single supermultiplet and generalize the Konishi operator, with implications for anomalous dimensions and three-point functions.

Contribution

It demonstrates that BMN operators with two charge defects are part of a single supermultiplet and extends the understanding of their structure and symmetries at finite charge J and in the BMN limit.

Findings

BMN operators form a single long supermultiplet.

BMN operators are large J generalizations of the Konishi operator.

Explicit construction of descendant operators and analysis of three-point functions.

Abstract

Implications of N=4 superconformal symmetry on Berenstein-Maldacena-Nastase (BMN) operators with two charge defects are studied both at finite charge J and in the BMN limit. We find that all of these belong to a single long supermultiplet explaining a recently discovered degeneracy of anomalous dimensions on the sphere and torus. The lowest dimensional component is an operator of naive dimension J+2 transforming in the [0,J,0] representation of SU(4). We thus find that the BMN operators are large J generalisations of the Konishi operator at J=0. We explicitly construct descendant operators by supersymmetry transformations and investigate their three-point functions using superconformal symmetry.