All-Order Amplitudes at any Multiplicity in the Multi-Regge Limit.

V. Del Duca,C. Duhr,S. Druc,G. Papathanasiou,F. Dulat,B. Verbeek,J. M. Drummond,R. Marzucca

doi:10.1103/physrevlett.124.161602

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.

Highlights

We propose an all-loop expression for scattering amplitudes in planar N 1⁄4 4 super Yang-Mills theory in multi-Regge kinematics valid for all multiplicities, all helicity configurations, and arbitrary logarithmic accuracy
Its S matrix exhibits a hidden dual conformal (DC) symmetry [1], which closes with the ordinary conformal symmetry into a Yangian algebra [2]
RN is trivial for N ≤ 5 [5], and is known analytically in general kinematics for N 1⁄4 6 through seven loops [6,7,8,9,10,11,12,13,14,15,16,17] and for N 1⁄4 7 through four loops [18,19,20,21,22], at the level of the symbol [8]

Summary

Introduction

We propose an all-loop expression for scattering amplitudes in planar N 1⁄4 4 super Yang-Mills theory in multi-Regge kinematics valid for all multiplicities, all helicity configurations, and arbitrary logarithmic accuracy. The dream of computing amplitudes analytically at any value of the coupling constant g2, or at least at any order in perturbation theory, has not yet been achieved.

Results

Conclusion