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 (13)

• Conformal properties of four-gluon planar amplitudes and Wilson loops
• The Pomeron and Gauge/String Duality
• 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
• The effect of NLO conformal spins in azimuthal angle decorrelation of jet pairs
• Iterated amplitudes in the high-energy limit
• 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 (42)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• Hexagon Wilson loop = six-gluon MHV amplitude
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• Bootstrapping an NMHV amplitude through three loops
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Higgs-regularized three-loop four-gluon amplitude in N=4 SYM: exponentiation and Regge limits
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• Adjoint BFKL at finite coupling: a short-cut from the collinear limit
• Integrability of scattering amplitudes in N=4 SUSY
• BFKL approach and six-particle MHV amplitude in N=4 super Yang-Mills
• A Cluster Bootstrap for Two-Loop MHV Amplitudes
• Sequential Discontinuities of Feynman Integrals and the Monodromy Group
• Iterated amplitudes in the high-energy limit
• Two-loop graviton scattering relation and IR behavior in N=8 supergravity
• Amplitudes meet Cosmology: A (Scalar) Primer
• Four-point Amplitudes in N=8 Supergravity and Wilson Loops
• Lifting Heptagon Symbols to Functions
• Mandelstam cuts and light-like Wilson loops in N=4 SUSY
• Excited Hexagon Wilson Loops for Strongly Coupled N=4 SYM
• Wilson loop OPE, analytic continuation and multi-Regge limit
• Critical gravitational collapse: towards a holographic understanding of the Regge region
• Bootstrapping six-gluon scattering in planar $\mathcal{N}=4$ super-Yang-Mills theory
• What can we learn about QCD and collider physics from N=4 super Yang-Mills?
• The SAGEX Review on Scattering Amplitudes, Chapter 7: Positive Geometry of Scattering Amplitudes
• Bootstrapping a Two-Loop Four-Point Form Factor
• The Two-Loop Remainder Function for Eight and Nine Particles
• Solution of the Bartels-Kwiecinski-Praszalowicz equation via Monte Carlo integration
• Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$ SYM theory in multi-Regge kinematics: Conformal Regge cut contribution
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• Infrared Safe Observables in $\mathcal{N}=4$ Super Yang-Mills Theory
• Regge meets collinear in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• Vacuum energy of the Bukhvostov-Lipatov model
• Heptagon Functions and Seven-Gluon Amplitudes in Multi-Regge Kinematics
• The two-loop Higgs impact factor
• Regge poles and cuts and the Lipatov vertex
• Twistors, strings and supersymmetric gauge theories
• An effective field theory approach for electroweak interactions in the high energy limit
• Discontinuities of multi-Regge amplitudes
• Exploring Reggeon bound states in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• MHV amplitudes, Wilson loops and the BDS ansatz in the superconformal N=2 QCD
• One-loop central-emission vertex for two gluons in $\mathcal{N}=4$ super Yang-Mills theory