Euler-Lagrange Equations for Effective Actions in QCD and Gravity at High Energies

Gluons in QCD and gravitons in quantum gravity lie on the Regge trajectories, which allows to formulate the high-energy scattering in these models in the framework of the reggeon field theory. In particular, the BFKL Pomeron is a composite state of reggeized gluons. In N = 4 SUSY the Pomeron is dual to the reggeized graviton living in the 10-dimensional anti-de-Sitter space. The effective actions for reggeized gluon and graviton interactions are formulated locally in the particle rapidities. The corresponding Euler-Lagrange equations are derived and their simple solutions are constructed.