Towards the three loop evolution equation for GPDs

Abstract

QCD in $d=4-2\epsilon$ dimensions and large number of flavors possesses a nontrivial infrared stable critical point. At the critical point the theory is invariant under the conformal transformations. It implies that the evolution kernel of leading-twist light-ray operators commutes with the generators of conformal transformations. Taking into account that the evolution kernels in the \rm{MS}-scheme are not sensitive to the space-time dimensions one concludes that QCD evolution equations in \rm{MS}-schemes have a hidden symmetry. Namely, the evolution kernel commutes with the generators of the conformal algebra. The explicit form of the generators differs from their canonical (classical) form and can be derived by studying conformal Ward identities. Invariance with respect to the conformal transformations imposes nontrivial constraints on the form of evolution kernels and allows one to restore the nonforward evolution kernels for the nonsinglet operators from the known NNLO anomalous dimensions. We present here the two loop expressions for the generators of conformal algebra.