Four loop anomalous dimension of the second moment of the non-singlet twist-2 operator in QCD

We present the result of a calculation for the first even moment of the non-singlet four-loop anomalous dimension of Wilson twist-2 operators in QCD with full color and flavor structures.Comment: 8 pages, comparison with prediction from Pade approximation (hep-ph/9905310) adde

Three-loop renormalization of the N=1, N=2, N=4 supersymmetric Yang-Mills theories

We calculate the renormalization constants of the N=1, N=2, N=4 supersymmetric Yang-Mills theories in an arbitrary covariant gauge in the dimensional reduction scheme up to three loops. We have found, that the beta-functions for N=1 and N=4 SYM theories are the same from the different triple vertices. This means that the dimensional reduction scheme works correctly in these models up to third order of perturbative theory.Comment: 6 page

Twist-three at five loops, Bethe Ansatz and wrapping

We present a formula for the five-loop anomalous dimension of N=4 SYM twist-three operators in the sl(2) sector. We obtain its asymptotic part from the Bethe Ansatz and finite volume corrections from the generalized Luescher formalism, considering scattering processes of spin chain magnons with virtual particles that travel along the cylinder. The complete result respects the expected large spin scaling properties and passes non-trivial tests including reciprocity constraints. We analyze the pole structure and find agreement with a conjectured resummation formula. In analogy with the twist-two anomalous dimension at four-loops, wrapping effects are of order log^2 M/M^2 for large values of the spin.Comment: 19 page

The 16th moment of the three loop anomalous dimension of the non-singlet transversity operator in QCD

We present the result of the three loop anomalous dimension of non-singlet transversity operator in QCD for the Mellin moment N=16. The obtained result coincides with the prediction from arXiv:1203.1022 and can serve as a confirmation of the correctness of the general expression for three loop anomalous dimension of non-singlet transversity operator in QCD for the arbitrary Mellin moment.Comment: 7 pages, 1 figure, minor changes in the tex

Five-Loop Anomalous Dimension of Twist-Two Operators

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 AdS5xS5 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 double-logarithmic 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.Comment: 43 pages; v2: references added, minor changes in the tex

Nonforward anomalous dimensions of Wilson operators in N=4 super-Yang-Mills theory

We present the next-to-leading order results for universal non-forward anomalous dimensions of Wilson twist-2 operators in N=4 supersymmetric Yang-Mills theory. The whole calculation was performed using supersymmetric Ward identities derived in this paper together with already known QCD results and does not involve any additional calculation of diagrams. We also considered one particular limit of our result, which could potentially be interesting in the context of AdS/CFT correspondence.Comment: 15 pages, references added, typos corrected, version accepted in JHE

Single impurity operators at critical wrapping order in the beta-deformed N=4 SYM

We study the spectrum of one single magnon in the superconformal beta-deformed N=4 SYM theory in the planar limit. We compute the anomalous dimensions of one-impurity operators O_{1,L}= tr(phi Z^{L-1}), including wrapping contributions at their critical order L.Comment: LaTeX, feynmf, Metapost, 20 pages, 11 figures, v2: results up to 11 loops completed, appendix on integral calculation extende

Four loop reciprocity of twist two operators in N=4 SYM

The four loop universal anomalous dimension of twist-2 operators in N=4 SYM has been recently conjectured. In this paper, we prove that it obeys a generalized Gribov-Lipatov reciprocity, previously known to hold at the three loop level.Comment: 15 pages, v3: Appendix A.3 added, main body shortened, version accepted in JHE