document: The reason to investigate the BFKL and DGLAP equations in the case of supersymmetric theories is based on a common belief, that the high symmetry may significantly simplify the structure of these equations. Indeed, it was found in the leading logarithmic approximation (LLA) [10], that the so-called quasi-partonic operators in N=1 SYM are unified in supermultiplets with anomalous dimensions obtained from universal anomalous dimensions γuni(j) by shifting its arguments by an integer number. Further, the anomalous dimension matrices for twist-2 operators are fixed by the superconformal invariance [10]. Calculations in the maximally extended N=4 SYM, where the coupling constant is not renormalized, give even more remarkable results. Namely, it turns out, that here all twist-2 operators enter in the same multiplet, their anomalous dimension matrix is fixed completely by the super-conformal invariance and its universal anomalous dimension in LLA is proportional to Ψ(j−1)−Ψ(1), which means, that the evolution equations for the matrix elements of quasi-partonic operators in the multicolor limit Nc→∞ are equivalent to the Schrödinger equation for an integrable Heisenberg spin model [11,12]. In QCD the integrability remains only in a small sector of the quasi-partonic operators [13]. In the case of N=4 SYM the equations for other sets of operators are also integrable [14–16]. Evolution equations for quasi-partonic operators are written in an explicitly super-conformal form in Ref. [17].
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