We present results for the three-loop universal anomalous dimension γ uni (j) of Wilson twist-2 operators in the N = 4 Supersymmetric Yang-Mills theory. These expressions are obtained by extracting the most complicated contributions from the three-loop anomalous dimensions in QCD. This result is in an agreement with the hypothesis of the integrability of N = 4 Supersymmetric Yang-Mills theory in the context of AdS/CFT-correspondence.

We prove that the validity of the recently proposed dressed, asymptotic Bethe ansatz for the planar AdS/CFT system is indeed limited at weak coupling by operator wrapping effects. This is done by comparing the Bethe ansatz predictions for the four-loop anomalous dimension of finite-spin twist-two operators to BFKL constraints from high-energy scattering amplitudes in N = 4 gauge theory. We find disagreement, which means that the ansatz breaks down for length-two operators at four-loop order. Our method supplies precision tools for multiple all-loop tests of the veracity of any yet-to-be constructed set of exact spectral equations. Finally we present a conjecture for the exact four-loop anomalous dimension of the family of twist-two operators, which includes the Konishi field.

We present the results of two-loop calculations of the anomalous dimension matrix for the Wilson twist-2 operators in the N=4 Supersymmetric Yang-Mills theory for polarized and unpolarized cases. This matrix can be transformed to a triangle form by the same similarity transformation as in the leading order. The eigenvalues of the anomalous dimension matrix are expressed in terms of an universal function with its argument shifted by integer numbers. In the conclusion we discuss relations between the weak and strong coupling regimes in the framework of the AdS/CFT correspondence.Comment: LaTeX file, 10 pages, no figure

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In this article we calculate the five-loop anomalous dimension of twist-two operators in the planar N = 4 SYM theory. Firstly, using reciprocity, we derive the contribution of the asymptotic Bethe ansatz. Subsequently, we employ the first finite-size correction for the AdS 5 × S 5 sigma model to determine the wrapping correction. The anomalous dimension found in this way passes all known tests provided by the NLO BFKL equation and doublelogarithmic constraints. This result thus furnishes an infinite number of experimental data for testing the veracity of the recently proposed spectral equations for planar AdS/CFT correspondence.