A preprint version of the article is available at ArXiv. The anomalous dimension of the twist four gluonic operator (74) in deep inelastic scattering is calculated in the double log approximation (DLA) of perturbative QCD. The result has also consequences on model building. Such operators lie on the unitarity bound and hence are conserved (irreducible) in the free theory. Anomalous dimensions of Wilson operators with large Lorentz spin scale logarithmically with the spin. Using a consistency condition derived from four-point correlation functions it is possible to birid the anomalous dimension of a composite operator phi(2). The technique relies on the known pattern of breaking of the irreducibility conditions in the interacting theory. We first compute contributions to anomalous dimensions of operators at dimension-six that arise at one-loop. Then we calculate two-loop anomalous dimensions for which the corresponding one-loop contribution is absent, using this powerful method. It turns Out that at N —~ 1 y 4(N— 1) is close to 272((N— 1)/2) where 72 is the anomalous dimension of the leading twist operator. Finally, the anomalous dimension of the singlet axial current is determined at O(1/N_f) by considering the renormalization of the anomaly in operator form. We present a recently developed method to constrain the anomalous dimension of scalar operators in a general Conformal Field Theory (CFT). Correspondingly, the renormalization group equation for Green functions with insertion of any combination of these local operators (at different space time points!) The anomalous dimensions below agree with literature [44, 45, 46] while the OPE coefficients are all new results. Critical exponents are computed for a variety of twist-2 composite operators, which occur in polarized and unpolarized deep inelastic scattering, at leading order in the 1/N ƒ expansion. The local composite operator A 2 is analysed in pure Yang–Mills theory in the Landau gauge within the algebraic renormalization. We compute the non-planar contribution to the universal anomalous dimension of the SU(4)-singlet twist-two operators in N=4 supersymmetric Yang-Mills theory at four loops through Lorentz spin eighteen. We extend and develop a method for perturbative calculations of anomalous dimensions and mixing matrices of leading twist conformal primary operators in conformal field theories. Recent multi-loop QCD calculations of twist-two anomalous dimensions revealed an existence of interesting structure behind the subleading corrections suppressed by powers of the Lorentz spin. It is proven that the anomalous dimension of A 2 is not an independent parameter, being expressed as a linear combination of the gauge β function and of the anomalous dimension of the gauge fields. will involve an anomalous dimension $$12 \times 12$$ matrix $$\gamma_{k\ell}$$ reflecting the operator mixing.