Properties of the Konishi multiplet in N=4 SYM theory

We study perturbative and non-perturbative properties of the Konishi multip let in N = 4 SYM theory in D = 4 dimensions. We compute two-, three- and fo ur-point Green functions with single and multiple insertions of the lowest component of the multiplet, K-1, and of the lowest component of the supercu rrent multiplet, Q(20)'. These computations require a proper definition of the renormalized operator, K-1, and lead to an independent derivation of it s 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 abo ve 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 exi stence of an operator belonging to the representation 20', which has vanish ing anomalous dimension at order g(2) and g(4) in perturbation theory as we ll as at the non-perturbative level, despite the fact that it does not obey any of the known shortening conditions.