本文研究了平面N = 4超对称Yang-Mills理论在特殊运动学中的散射振幅，其中所有外部四维动量都限制在一个（1+1）维子空间中.的振幅是已知的，以满足非平凡的因式分解所产生的多共线的限制，我们在这里进一步研究。我们能够找到这些多重共线极限的一般解。这就得到了一个简单的公式，它用函数S_m的线性组合来表示n点超振幅，这些函数在所有适当的多重共线极限中被限制为零。这些共线消失的构建块S_m是依赖于具有8 \leq m \leq 4 l的简化m点运动学的对偶共形不变函数。对于MHV振幅，可以直接使用例如参考文献[1]中的方法来构建它们。这个过程提供了一个普遍的提升较低的点共线消失的积木S_m的所有较高的点振幅。它在任何环路电平1 \geq 1和任何MHV或N^kMHV幅度下工作。我们比较这与明确的例子，涉及n点MHV振幅在2个循环和10点MHV振幅在3个循环。树级超级振幅具有不同的属性，并在我们的方法中从循环级振幅分开处理。为了说明这一点，我们推导出一个表达式的n点树级NMHV振幅在特殊的运动学。
英文摘要：
We consider scattering amplitudes in planar N = 4 supersymmetric Yang-Mills theory in special kinematics where all external four-dimensional momenta are restricted to a (1+1)-dimensional subspace. The amplitudes are known to satisfy non-trivial factorisation properties arising from multi-collinear limits, which we further study here. We are able to find a general solution to these multi-collinear limits. This results in a simple formula which represents an n-point superamplitude in terms of a linear combination of functions S_m which are constrained to vanish in all appropriate multi-collinear limits. These collinear-vanishing building blocks, S_m, are dual-conformally-invariant functions which depend on the reduced m-point kinematics with 8 \leq m \leq 4l. For MHV amplitudes they can be constructed directly using, for example, the approach in Ref. [1]. This procedure provides a universal uplift of lower-point collinearly vanishing building blocks S_m to all higher-point amplitudes. It works at any loop-level l \geq 1 and for any MHV or N^kMHV amplitude. We compare this with explicit examples involving n-point MHV amplitudes at 2-loops and 10-point MHV amplitudes at 3-loops. Tree-level superamplitudes have different properties and are treated separately from loop-level amplitudes in our approach. To illustrate this we derive an expression for n-point tree-level NMHV amplitudes in special kinematics.
