论文标题
示意图
The Diagrammatic Coaction
论文作者
论文摘要
图解的共同负责是Feynman积分，其切割和他们承认的微分方程的分析结构。该共胶将任何图表映射到其捏和切割的张量产物中。这些分别对应于定义主积分的差分形式，以及将繁殖子的子集放在壳上的集成轮廓。在规范的基础上，这些形式和轮廓是彼此双重的。在这次演讲中，我回顾了我们对这种代数结构的当前理解及其对尺寸调节的Feynman积分的表现，这些积分可扩展到整数尺寸周围的小聚集体。使用一环和两环的积分示例，我将解释形式和轮廓之间的二元性，以及作用于维度调节剂中劳伦系数的局部共同行为与对广义超角度函数作用的全局均值。
The diagrammatic coaction underpins the analytic structure of Feynman integrals, their cuts and the differential equations they admit. The coaction maps any diagram into a tensor product of its pinches and cuts. These correspond respectively to differential forms defining master integrals, and integration contours which place a subset of the propagators on shell. In a canonical basis these forms and contours are dual to each other. In this talk I review our present understanding of this algebraic structure and its manifestation for dimensionally-regularized Feynman integrals that are expandable to polylogarithms around integer dimensions. Using one- and two-loop integral examples, I will explain the duality between forms and contours, and the correspondence between the local coaction acting on the Laurent coefficients in the dimensional regulator and the global coaction acting on generalised hypergeometric functions.
