NNLO classical solution for Lipatov’s effective action for reggeized gluons

Abstract

We consider the formalism of small-[Formula: see text] effective action for reggeized gluons[Formula: see text] 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.