Narrow Results

In this paper we derive Dyson–Schwinger hierarchy of the equations for the correlators of reggeized gluon fields in the framework of Lipatov’s high energy QCD effective action formalism.${}^{1\text{–}10}$ The explicit perturbative expressions for the correlators till correlator of four Reggeon fields inclusively are obtained and different perturbative schemes for the solutions of the equation for the two-field correlator are discussed. A correspondence between the correlators of reggeized gluon fields and Wilson line operators of longitudinal gluon field is established with the help of the results of Ref. 10. The connection between the JIMWLK-Balitsky formalism and Lipatov’s effective action approach and applications of the obtained results are also discussed.

We consider the formalism of small-$x$ effective action for reggeized gluons${}^{1\text{–}10}$ and, following the approach developed in Refs. 11–17, calculate the classical gluon field to NNLO precision with fermion loops included. It is demonstrated that for each perturbative order, the self-consistency of the equations of motion is equivalent to the transversality conditions applied to the solution of the equations, these conditions allow to construct the general recursive scheme for the solution’s calculation. The one fermion loop contribution to the classical solutions and application of the obtained results are also discussed.