Properties of the Konishi multiplet in N=4 SYM theory

TL;DR

This paper investigates the properties of the Konishi multiplet in N=4 SYM theory, computing correlation functions, anomalous dimensions, and confirming the existence of a unique operator with vanishing anomalous dimension.

Contribution

It provides a detailed perturbative and non-perturbative analysis of the Konishi multiplet, including new computations of correlators and operator dimensions, and identifies a novel operator with special properties.

Findings

Computed two-, three-, and four-point Green functions involving the Konishi multiplet.

Confirmed the anomalous dimension of the Konishi operator matches previous results.

Identified an operator in the 20' representation with zero anomalous dimension at multiple orders.

Abstract

We study perturbative and non-perturbative properties of the Konishi multiplet in N=4 SYM theory in D=4 dimensions. We compute two-, three- and four-point Green functions with single and multiple insertions of the lowest component of the multiplet, and of the lowest component of the supercurrent multiplet. These computations require a proper definition of the renormalized operator and lead to an independent derivation of its anomalous dimension. The O(g^2) value found in this way is in agreement with previous results. We also find that instanton contributions to the above correlators vanish. From our results we are able to identify some of the lowest dimensional gauge-invariant composite operators contributing to the OPE of the correlation functions we have computed. We thus confirm the existence of an operator belonging to the representation 20', which has vanishing anomalous dimension at order g^2 and g^4 in perturbation theory as well as at the non-perturbative level, despite the fact that it does not obey any of the known shortening conditions.