All-order amplitudes at any multiplicity in the multi-Regge limit

Abstract

We propose an all-loop expression for scattering amplitudes in planar N=4 super Yang-Mills theory in multi-Regge kinematics valid for all multiplicities, all helicity configurations and arbitrary logarithmic accuracy. Our expression is arrived at from comparing explicit perturbative results with general expectations from the integrable structure of a closely related collinear limit. A crucial ingredient of the analysis is an all-order extension for the central emission vertex that we recently computed at next-to-leading logarithmic accuracy. As an application, we use our all-order formula to prove that all amplitudes in this theory in multi-Regge kinematics are single-valued multiple polylogarithms of uniform transcendental weight.

arXiv comment6 pages, 2 figures, 2 ancillary files; v2: minor corrections and clarifications, matches published version

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• How tropical are seven- and eight-particle amplitudes?
• Lifting Heptagon Symbols to Functions
• Multi-Regge Limit of the Two-Loop Five-Point Amplitudes in $\mathcal{N}=4$ Super Yang-Mills and $\mathcal{N}=8$ Supergravity
• 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
• Coaction and double-copy properties of configuration-space integrals at genus zero
• Bootstrapping a Two-Loop Four-Point Form Factor
• The Two-Loop Remainder Function for Eight and Nine Particles
• Anomalous Dimensions from Soft Regge Constants
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• A Collinear Perspective on the Regge Limit
• Dynamical Spin Chains in 4D $\mathcal{N}=2$ SCFTs
• Heptagon Functions and Seven-Gluon Amplitudes in Multi-Regge Kinematics
• A Two-Loop Four-Point Form Factor at Function Level
• The two-loop Higgs impact factor
• One-loop impact factor for the emission of two gluons
• Regge poles and cuts and the Lipatov vertex
• The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes
• Exploring Reggeon bound states in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• A construction of single-valued elliptic polylogarithms
• One-loop central-emission vertex for two gluons in $\mathcal{N}=4$ super Yang-Mills theory