Geodesic
Double-logarithmic asymptotics of scattering amplitudes in gravity and supergravity
Teoretičeskaâ i matematičeskaâ fizika, Tome 175 (2013) no. 3, pp. 408-418

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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.
Keywords: quantum gravity, high-energy asymptotic behavior, behavior of Regge-type amplitudes, double-logarithmic approximation. 
@article{TMF_2013_175_3_a8,
     author = {L. N. Lipatov},
     title = {Double-logarithmic asymptotics of scattering amplitudes in gravity and supergravity},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {408--418},
     publisher = {mathdoc},
     volume = {175},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2013_175_3_a8/}
}
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L. N. Lipatov. Double-logarithmic asymptotics of scattering amplitudes in gravity and supergravity. Teoretičeskaâ i matematičeskaâ fizika, Tome 175 (2013) no. 3, pp. 408-418. http://geodesic.mathdoc.fr/item/TMF_2013_175_3_a8/