The dimensionally reduced description of the high energy scattering and the effective action for the reggeized gluons

We discuss the high energy scattering of hadrons with the multi-Regge kinematics. The effective 2D model for the interaction between the produced hard gluons appears as a result of the dimensional reduction, which is similar to the dimensional reduction 3 + 1 D → 3 D of the high temperature gauge theory. It is demonstrated that being supplemented by the exchange by virtual 3 + 1 D gluons this 2D model gives rise to the hermitian version of the effective action of Lipatov for the interaction between the ordinary and the reggeized gluons.