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Next-to-leading order evolution of twist-two conformal operators: The abelian case

We present the method, based on the use of the broken conformal Ward identities, for the calculation of the anomalous dimensions of conformal operators beyond the leading order of perturbation theory. By means of this technique we find the complete set of two-loop corrections to the off-diagonal elements of the anomalous dimension matrix (the diagonal ones are known from deep inelastic scattering calculations) of the parity odd and even singlet local operators in the Abelian gauge theory. We reconstruct corresponding exclusive two-loop evolution kernels and give the reduction formulae for the restoration of the diagonal part of the ER-BL kernels from the DGLAP splitting functions.