Lev N. Lipatov

The scattering amplitudes in QCD and gravity at high energies are described in terms of reggeized gluons and gravitons, respectively. In particular, the BFKL Pomeron in N = 4 SUSY is dual to the reggeized graviton living in the 10-dimensional anti-de-Sitter space. The effective actions for the reggeized gluons and gravitons are local in their rapidities. The Euler-Lagrange equations for these effective theories are constructed and their solutions are used for calculations of corresponding Reggeon vertices and trajectories.

We review the Sudakov results on the double logarithmic asymptotics of the electron form-factor which were based on his parametrization of the virtual particle momenta in the Feynman diagrams. The high energy amplitudes for various QED and QCD processes in the double-logarithmic approximation are obtained by using the Bethe-Salpeter approach and the evolution equations. The ultraviolet divergency of the graviton Regge trajectory allows to derive the infrared evolution equation for the graviton-graviton scattering amplitude with a double-logarithmic accuracy. The asymptotic behavior of this amplitude depends essentially on the rank N of the super-symmetry.

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.

EPJ Web of Conferences, open-access proceedings in physics and astronomy

We describe the (universal) Green function for the discrete BFKL pomeron with running coupling and infrared boundary conditions and discuss the significance of the discrete poles in the case of Deep Inelastic Scattering.