BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes

Abstract

After a brief review of the BFKL approach to Regge processes in QCD and in supersymmetric (SUSY) gauge theories we propose a strategy for calculating the next-to-next-to-leading order corrections to the BFKL kernel. They can be obtained in terms of various cross-sections for Reggeized gluon interactions. The corresponding amplitudes can be calculated in the framework of the effective action for high energy scattering. In the case of N=4 SUSY it is also possible to use the Bern-Dixon-Smirnov (BDS) ansatz. For this purpose the analytic properties of the BDS amplitudes at high energies are investigated, in order to verify their self-consistency. It is found that, for the number of external particles being larger than five, these amplitudes, beyond one loop, are not in agreement with the BFKL approach which predicts the existence of Regge cuts in some physical channels.

41 pages, expanded version with many clarifications and new references, conclusions unchanged. Note added

References in corpus (9)

• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
• Dressing and Wrapping
• Regge behavior of gluon scattering amplitudes in N=4 SYM theory
• The dipole form of the BFKL kernel in supersymmetric Yang--Mills theories

Cited by in corpus (7)

• Hexagon Wilson loop = six-gluon MHV amplitude
• Integrability of scattering amplitudes in N=4 SUSY
• Two-loop graviton scattering relation and IR behavior in N=8 supergravity
• Four-point Amplitudes in N=8 Supergravity and Wilson Loops
• Critical gravitational collapse: towards a holographic understanding of the Regge region
• Twistors, strings and supersymmetric gauge theories
• MHV amplitudes, Wilson loops and the BDS ansatz in the superconformal N=2 QCD