Euler-Lagrange equations for high energy actions in QCD and in gravity

The high energy scattering in QCD and gravity can be described in terms of reggeized gluons and gravitons, respectively. At N = 4 SUSY the BFKL Pomeron is dual to the reggeized graviton living in the 10-dimensional anti-de-Sitter space. We discuss the corresponding effective actions for reggeized gluon and graviton interactions. The Euler-Lagrange equations for these effective theories are constructed with a variational approach and by using an invariance under the gauge and general coordinate transformations. We discuss their solutions and applications to the calculation of effective Reggeon vertices and trajectories.