The one-instanton contributions to various correlation functions of superconformal currents in four-dimensional N = 4 supersymmetric SU(2) Yang-Mills theory are evaluated to the lowest order in perturbation theory. Expressions of the same form are obtained from the leading effects of a single D-instanton extracted from the IIB superstring effective action around the AdS 5 × S 5 background. This is in line with the suggested AdS/YangMills correspondence. The relation between Yang-Mills instantons and Dinstantons is further confirmed by the explicit form of the classical D-instanton solution in the AdS 5 × S 5 background and its associated supermultiplet of zero modes. Speculations are made concerning instanton effects in the large-N c limit of the SU(N c ) Yang-Mills theory.

We compute four-point correlation functions of scalar composite operators in the N =4 supercurrent multiplet at order g 4 using the N =1 superfield formalism. We confirm the interpretation of short-distance logarithmic behaviours in terms of anomalous dimensions of unprotected operators exchanged in the intermediate channels and we determine the two-loop contribution to the anomalous dimension of the N =4 Konishi supermultiplet.

We show that the logarithmic behaviour seen in perturbative and non perturbative contributions to Green functions of gauge-invariant composite operators in N =4 SYM with SU (N ) gauge group can be consistently interpreted in terms of anomalous dimensions of unprotected operators in long multiplets of the superconformal group SU (2, 2|4). In order to illustrate the point we analyse the short-distance behaviour of a particularly simple four-point Green function of the lowest scalar components of the N =4 supercurrent multiplet. Assuming the validity of the Operator Product Expansion, we are able to reproduce the known value of the one-loop anomalous dimension of the single-trace operators in the Konishi supermultiplet. We also show that it does not receive any non-perturbative contribution from the one-instanton sector. We briefly comment on double-and multi-trace operators and on the bearing of our results on the AdS

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 fourpoint Green functions with single and multiple insertions of the lowest component of the multiplet, K 1 , and of the lowest component of the supercurrent multiplet, Q 20 ′ . These computations require a proper definition of the renormalized operator, K 1 , 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 gaugeinvariant 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.

We study a marginal deformation of N = 4 Yang-Mills, with a real deformation parameter β. This β-deformed model has only N = 1 supersymmetry and a U(1)×U(1) flavor symmetry. The introduction of a new superspace ⋆-product allows us to formulate the theory in N = 4 light-cone superspace, despite the fact that it has only N = 1 supersymmetry. We show that this deformed theory is conformally invariant, in the planar approximation, by proving that its Green functions are ultra-violet finite to all orders in perturbation theory.