Using N = 1 superspace techniques in four dimensions we show how to perturbatively compute the superpotential generated for the glueball superfield upon integrating out massive charged fields. The technique applies to arbitrary gauge groups and representations. Moreover we show that for U (N ) gauge theories admitting a large N expansion the computation dramatically simplifies and we prove the validity of the recently proposed recipe for computation of this quantity in terms of planar diagrams of matrix integrals. November, 2002

In a N = 1 superspace formulation of N = 4 Yang-Mills theory we obtain the anomalous dimensions of chiral operators with large R charge J → ∞ keeping g 2 N/J 2 finite, to all orders of perturbation theory in the planar limit. Our result proves the conjecture that the anomalous dimensions are indeed finite in the above limit. This amounts to an exact check of the proposed duality between a sector of N = 4 Yang-Mills theory with large R charge J and string theory in a pp-wave background.

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In this paper we give all the details of the calculation that we presented in our previous paper arXiv:0712.3522, concerning the four-loop anomalous dimension of the Konishi descendant tr(φZφZ − φφZZ) in the SU(2) sector of the N = 4 planar SYM theory. We explicitly consider all the wrapping diagrams that we compute using an N = 1 superspace approach and Gegenbauer polynomial x-space techniques.