We investigate configuration-space integrals over punctured Riemann spheres from the viewpoint of the motivic Galois coaction and double-copy structures generalizing the Kawai-Lewellen-Tye (KLT) relations in string theory. For this purpose, explicit bases of twisted cycles and cocycles are worked out whose orthonormality simplifies the coaction. We present methods to efficiently perform and organize the expansions of configuration-space integrals in the inverse string tension α′ or the dimensional-regularization parameter ϵ of Feynman integrals. Generating-function techniques open up a new perspective on the coaction of multiple polylogarithms in any number of variables and analytic continuations in the unintegrated punctures. We present a compact recursion for a generalized KLT kernel and discuss its origin from intersection numbers of Stasheff polytopes and its implications for correlation functions of two-dimensional conformal field theories. We find a non-trivial example of correlation functions in (\( \mathfrak{p} \), 2) minimal models, which can be normalized to become uniformly transcendental in the \( \mathfrak{p} \) → ∞ limit.

我们从动机Galois互作用和在弦论中概括了Kawai-Lewellen-Tye（KLT）关系的双副本结构的角度，研究了穿孔Riemann球上的构型空间积分。为此，找出了扭曲周期和同周期的显式基础，它们的正交性简化了协作。我们本发明的方法有效地进行，并组织结构空间积分的膨胀在逆弦的张力α '或二维正则化参数ε费曼积分。生成函数技术为多个多对数在任意数量的变量中的协同作用以及未整合穿刺中的解析连续性开辟了新的视角。我们提出了一个广义KLT核的紧凑递归，并讨论了它的起源于Stasheff多边形的相交数及其对二维共形场理论相关函数的影响。我们在（\（\ mathfrak {p} \）， 2）最小模型中找到相关函数的重要例子，可以将其归一化以在\（\ mathfrak {p} \） →∞极限内变得统一超越。