A. V. Kotikov

Three-loop universal anomalous dimension of the Wilson operators in N = 4 SUSY Yang-Mills model

Abstract We present results for the three-loop universal anomalous dimension γuni(j) of Wilson twist-2 operators in the N =4 Supersymmetric Yang–Mills model. These expressions are obtained by extracting the most complicated contributions from the three loop non-singlet anomalous dimensions in QCD which were calculated recently. Their singularities at j=1 coincide with the predictions obtained from the BFKL equation for N =4 SYM in the next-to-leading order. The asymptotics of γuni(j) at large j is in an agreement with the expectations based on an interpolation between week and strong coupling regimes in the framework of the AdS/CFT correspondence.

DGLAP and BFKL equations in the

We discuss DGLAP and BFKL evolution equations in the N = 4 supersymmetric gauge theory in the leading and next-to-leading approximations. Eigenvalues of the BFKL kernel in this model turn out to be analytic functions of the conformal spin. It allows us to find the residues of the anomalous dimensions of the twist-2 operators in the points j = 1, 0,−1, .... from the BFKL equation in an agreement with their direct calculation from the DGLAP equation. The holomorphic separability of the BFKL kernel and the integrability of the DGLAP dynamics in this model are also discussed. PACS: 12.38.Bx

N=4

Abstract 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 end we discuss relations between the weak and strong coupling regimes in the framework of the AdS/CFT correspondence.

supersymmetric gauge theory

Abstract. The aim of this paper is to summarize the general status of our understanding of small-x physics. It is based on presentations and discussions at an informal meeting on this topic held in Lund, Sweden, in March 2001. This document also marks the founding of an informal collaboration between experimentalists and theoreticians with a special interest in small-x physics. This paper is dedicated to the memory of Bo Andersson, who died unexpectedly from a heart attack on March 4th, 2002.The aim of this paper is to summarize the general status of our understanding of small-x physics. It is based on presentations and discussions at an informal meeting on this topic held in Lund, Sweden, in March 2001. This document also marks the founding of an informal collaboration between experimentalists and theoreticians with a special interest in small-x physics. This paper is dedicated to the memory of Bo Andersson, who died unexpectedly from a heart attack on March 4th, 2002.

Anomalous dimensions of Wilson operators in N=4 SYM theory

Abstract We investigate the Eden–Staudacher equation for the anomalous dimension of the twist-2 operators at the large spin s in the N = 4 super-symmetric gauge theory. This equation is reduced to a set of linear algebraic equations with the kernel calculated analytically. We prove that in perturbation theory the anomalous dimension is a sum of products of the Euler functions ζ ( k ) having the property of the maximal transcendentality with the coefficients being integer numbers. The radius of convergency of the perturbation theory is found. It is shown, that at g = ∞ the kernel has an essential singularity. The analytic properties of the solution of the Eden–Staudacher equation are investigated. In particular for the case of the strong coupling constant the solution has an essential singularity on the second sheet of the variable j appearing in its Laplace transformation. Similar results are derived also for the Beisert–Eden–Staudacher equation which includes the contribution from the phase related to the crossing symmetry of the underlying S -matrix. We show, that its singular solution at large coupling constants reproduces the anomalous dimension predicted from the string side of the AdS/CFT correspondence.

Small x phenomenology: Summary and status

Abstract We present the results of the next-to-next-to-leading order QCD analysis of the recently revised experimental data of the CCFR collaboration for the xF 3 structure function using the Jacobi polynomial expansion method. The effects of the higher twist contributions are included into the fits following the infrared renormalon motivated model. The special attention is paid to the checks of the predictive abilities of the infrared renormalon model and to the independent extractions of the x -dependent shape of the twist-4 contributions to the xF 3 structure function in the process of the leading order, next-to-leading order and next-to-next-to-leading order fits of the revised CCFR data. We stress that at the next-to-next-to-leading order the results for α s ( M Z ) turn out to be almost nonsensitive to the higher-twist terms. We obtain the following result α s NNLO ( M Z )=0.117±0.002(stat)±0.005(syst)±0.003(theory). The comparison of the outcomes of our next-to-leading order and next-to-next-to-leading order analysis indicate that the theoretical QCD uncertainties were underestimated in the process of the next-to-leading order determination of α s ( M Z ), made recently by the CCFR collaboration itself.We present the results of the next-to-next-to-leading order QCD analysis of the recently revised experimental data of the CCFR collaboration for the

On the highest transcendentality in N = 4 SUSY ∗

xF_3

NEXT-TO-NEXT-TO-LEADING ORDER QCD ANALYSIS OF THE REVISED CCFR DATA FOR XF3 STRUCTURE FUNCTION AND THE HIGHER TWIST CONTRIBUTIONS

structure function using the Jacobi polynomial expansion method. The effects of the higher twist contributions are included into the fits following the infrared renormalon motivated model. The special attention is paid to the checks of the predictive abilities of the infrared renormalon model and to the independent extraction of the

Analytic three-loop Solutions for N = 4 SYM Twist Operators

x

Pomeron in the N=4 supersymmetric gauge model at strong couplings

-shape of the twist-4 contributions to the