Double-logarithmic asymptotics of scattering amplitudes in gravity and supergravity

We review the Balitsky–Fadin–Kuraev–Lipatov approach to high-energy scattering in QCD and supersymmetric gauge theories. At a large number of colors, the equations for the gluon composite states in the $t$-channel have remarkable mathematical properties including their Möbius invariance, holomorphic separability, duality symmetry, and integrability. We formulate a theory of Reggeized gluon interactions in the form of a gauge-invariant effective action local in particle rapidities. In the maximally extended $N=4$ supersymmetry, the Pomeron is dual to the Reggeized graviton in the ten-dimensional anti-de Sitter space. As a result, the Gribov Pomeron calculus should be reformulated here as a generally covariant effective field theory for the Reggeized gravitons. We construct the corresponding effective action, which allows calculating the graviton Regge trajectory and its couplings. We sum the double-logarithmic contributions for amplitudes with graviton quantum numbers in the $t$-channel in the Einstein–Hilbert gravity and its supersymmetric generalizations. As the supergravity rank $N$ increases, the double-logarithmic amplitudes begin to decrease rapidly compared with their Born contributions.