QCD evolution equations

Abstract

We discuss QCD evolution equations for two and three particle correlation functions of quarks and gluon fields in a hadron which describe development of the momentum distribution of a parton system with a change of the wave length of a probe which resolves it. We show in a general case of two-particle correlators how the four-dimensional conformal algebra and the known pattern of conformal symmetry breaking in QCD can be used to solve the complicated mixing problem of local operators under renormalization and compute economically anomalous dimensions of quark and gluon composite operators. An extension of QCD to N = 1 super Yang-Mills theory and use of superconformal anomalies arising after quantization allows to derive non-trivial relations between the anomalous dimensions. For three-parton systems the conformal symmetry alone is not enough to solve the three-particle problem. We show that in milticolor limit of QCD there arises an extra conserved charge describing the solitonic motion of the system of particles. The problem admits a one-to-one correspondence with certain spin chain models which are exactly solvable.