Properties of the Konishi multiplet in N=4 SYM theory

TL;DR

This paper investigates the N=4 SYM Konishi multiplet, constructing its full structure including the Konishi anomaly, and analyzes perturbative and non-perturbative properties through explicit correlation functions involving the Konishi scalar K1 and protected Q_{20'} operators. By renormalizing K1 and computing two-, three-, and four-point functions to O(g^2) (and leveraging known O(g^4) results), the authors extract anomalous dimensions via OPE-based constraints and reveal a protected 20' scalar with vanishing anomalous dimension up to O(g^4) and non-perturbatively. They also show instanton contributions to these correlators vanish, implying absence of non-perturbative corrections to the Konishi anomalous dimension in the studied sectors and highlighting intriguing non-renormalization features consistent with AdS/CFT expectations. The work provides bounds on operator dimensions in the 20' and singlet sectors and discusses implications for symmetry structures like the U_B(1) bonus symmetry and SL(2,Z) duality. Overall, it reinforces the nuanced interplay between conformal invariance, operator mixing, and non-perturbative effects in N=4 SYM and its holographic duals.

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.