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.

中文翻译：

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在多Regge极限中任何多重的所有阶振幅

我们提出了一个全环表达式，用于散射平面中的振幅 $𝒩=4$在多Regge运动学中的超级杨米尔斯理论对所有多重性，所有螺旋性配置和任意对数精度均有效。我们的表达是通过将显式扰动结果与密切相关的共线极限的可积结构的一般期望进行比较而得出的。分析的关键要素是对中心发射顶点的全阶扩展，我们最近以对数精度为准的精确度对其进行了计算。作为一种应用，我们使用全阶公式来证明该理论在多Regge运动学中的所有振幅都是均等的先验权重的单值多个多对数。