发表机构
The University of Edinburgh; University of Amsterdam; Queen Mary University of London（爱丁堡大学; 阿姆斯特丹大学; 伦敦玛丽女王大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种基于Landau分析的策略，通过识别分支点并跟踪解析延拓来递归构造多重多对数积分的符号，并给出高效算法，用于计算扭曲超平面排列上有限积分的符号，可应用于共形耦合理论中宇宙学关联函数的任意阶计算。
AI 中文摘要
我们提出了一种受Landau分析启发的策略，用于直接计算在扭曲上同调中求值为多重多对数的积分的符号。核心思想是识别当外部参数变化时，奇异超曲面、扭曲超曲面和积分边界可能相互作用的所有方式，从而产生对数或代数分支点。通过跟踪积分在其每个分支点周围解析延拓时如何被修改，我们可以递归地构造其符号。我们通过概述一种高效算法来阐述这种方法，该算法用于计算扭曲超平面排列上的有限积分在围绕扭曲参数特殊值展开时的符号。该算法可用于计算共形耦合理论中宇宙学关联函数的（超越）被积函数，直至扭曲展开的任意阶。
英文摘要
We propose a Landau-analysis-inspired strategy for directly computing the symbol of integrals that evaluate to multiple polylogarithms in twisted cohomology. The central idea is to identify all ways in which singular hypersurfaces, twisted hypersurfaces, and integration boundaries can interact when external parameters are varied, giving rise to logarithmic or algebraic branch points. By tracking how an integral is modified when analytically continued around each of its branch points, we can recursively construct its symbol. We illustrate this approach by outlining an efficient algorithm for computing the symbol of finite integrals over twisted hyperplane arrangements, when they are expanded around special values of the twist parameter. This algorithm can be used to compute the (transcendental) integrands of cosmological correlators in conformally coupled theories to any order in the twist expansion.
Comments18 pages, 10 figures. Ancillary Mathematica code included
