Double-logarithmic asymptotics of scattering amplitudes in gravity and supergravity. (English. Russian original) Zbl 1286.83043
Theor. Math. Phys. 175, No. 3, 788-796 (2013); translation from Teor. Mat. Fiz. 175, No. 3, 408-418 (2013).
Summary: 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.
MSC:
| 83C45 | Quantization of the gravitational field |
| 83E50 | Supergravity |
| 81U05 | \(2\)-body potential quantum scattering theory |
Keywords:
quantum gravity; high-energy asymptotic behavior; behavior of Regge-type amplitudes; double-logarithmic approximationReferences:
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