The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit

Abstract

We review the Regge and multi-Regge limit of scattering amplitudes in gauge theory, focusing on QCD and its maximally supersymmetric cousin, planar $\mathcal{N}=4$ super-Yang-Mills theory. We identify the large logarithms that are developed in these limits, and the progress that has been made in resumming them, towards next-to-next-to-leading logarithms for BFKL evolution in QCD, as well as all-orders proposals in planar $\mathcal{N}=4$ super-Yang-Mills theory and the perturbative checks of those proposals. We also cover the application of single-valued multiple polylogarithms to this important kinematical limit of particle scattering.

50 pages, 9 figures, see also the overview article arXiv:2203.13011. v3: typo's corrected, journal version

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• Classical Polylogarithms for Amplitudes and Wilson Loops
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• 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
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• An Operator Product Expansion for Polygonal null Wilson Loops
• Bootstrapping an NMHV amplitude through three loops
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
• A Test of the AdS/CFT Correspondence Using High-Spin Operators
• Bootstrapping the QCD soft anomalous dimension
• Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• Four-gluon scattering at three loops, infrared structure and Regge limit
• Proof of the multi-Regge form of QCD amplitudes with gluon exchanges in the NLA
• 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
• Analyzing high-energy factorization beyond next-to-leading logarithmic accuracy
• Four-loop collinear anomalous dimensions in QCD and $\mathcal{N}=4$ super Yang-Mills
• Three-Loop Leading Singularities and BDS Ansatz for Five Particles
• New Dual Conformally Invariant Off-Shell Integrals
• Excited Hexagon Wilson Loops for Strongly Coupled N=4 SYM
• Four-Loop Collinear Anomalous Dimension in N = 4 Yang-Mills Theory
• Scattering amplitudes in the Regge limit and the soft anomalous dimension through four loops
• ${\gamma }^{\ast }{\gamma }^{\ast }$ Cross Section at NLO and Properties of the BFKL Evolution at Higher Orders
• Multi-Regge Limit of the n-Gluon Bubble Ansatz
• The gluon Regge trajectory at three loops from planar Yang-Mills theory
• Climbing three-Reggeon ladders: four-loop amplitudes in the high-energy limit in full colour
• Heptagon Amplitude in the Multi-Regge Regime
• Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$ SYM theory in multi-Regge kinematics: Conformal Regge cut contribution
• Regge meets collinear in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• Heptagon Functions and Seven-Gluon Amplitudes in Multi-Regge Kinematics
• Exploring Reggeon bound states in strongly-coupled $\mathcal{N}=4$ super Yang-Mills

Cited by in corpus (4)

• The SAGEX Review on Scattering Amplitudes
• Conformal graphs as twisted partition functions
• Single-valued representation of unpolarized and polarized semi-inclusive deep inelastic scattering at next-to-next-to-leading order
• Analytic structure of the high-energy gravitational amplitude: multi-H diagrams and classical 5PM logarithms