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TMF, 2013, Volume 175, Number 3, Pages 408–418 (Mi tmf8489)  

Double-logarithmic asymptotics of scattering amplitudes in gravity and supergravity

L. N. Lipatov

Petersburg Nuclear Physics Institute, Gatchina, St. Petersburg, Russia

Abstract: 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

DOI: https://doi.org/10.4213/tmf8489

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English version:
Theoretical and Mathematical Physics, 2013, 175:3, 788–796

Bibliographic databases:


Citation: L. N. Lipatov, “Double-logarithmic asymptotics of scattering amplitudes in gravity and supergravity”, TMF, 175:3 (2013), 408–418; Theoret. and Math. Phys., 175:3 (2013), 788–796

Citation in format AMSBIB
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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