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Double-logarithmic asymptotics of scattering amplitudes in gravity and supergravity

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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.

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Correspondence to L. N. Lipatov.

Additional information

Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 175, No. 3, pp. 408–418, June, 2013.

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Lipatov, L.N. Double-logarithmic asymptotics of scattering amplitudes in gravity and supergravity. Theor Math Phys 175, 788–796 (2013). https://doi.org/10.1007/s11232-013-0065-6

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Keywords

  • quantum gravity
  • high-energy asymptotic behavior
  • behavior of Regge-type amplitudes
  • double-logarithmic approximation