BMN Operators and Superconformal Symmetry

TL;DR

The paper demonstrates that BMN operators with two defects form a single long N=4 superconformal multiplet, with the primary transforming in the [0,J,0] representation and having naive dimension J+2. By employing a D=9+1 superspace and a harmonic superspace formalism, Beisert constructs explicit finite-J BMN primaries and their bosonic descendants, showing their anomalous dimensions are degenerate across operator flavors in the BMN limit. The work further derives superconformal constraints on two- and three-point functions involving BMN operators, clarifying operator mixing (single-trace vs. double-trace) and providing explicit structure constants in several correlator configurations, including a BMN-limit expression for extremal correlators. Overall, the results supply a representation-theory–driven, symmetry-based dictionary for BMN operators, their mixing, and their correlation functions, bridging finite-J gauge theory data with the plane-wave string regime and Konishi-like operators at small J. This framework deepens the understanding of AdS/CFT in the plane-wave limit and suggests a universal, defect-number–based organization of local operators in N=4 SYM beyond the BMN approximation.

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.