KZB方程的两种方言：生成单圈开弦积分
Two dialects for KZB equations: generating one-loop open-string integrals
摘要：
\rcites{Mafra:2019xms, *Mafra:2019ddf, Broedel:2019gba}中提出了两种不同的结构，它们产生了单圈开弦振幅中的genus-one位形空间积分的低能展开。我们将证明这两种方法都可以追溯到Knizhnik-Zamolodchikov-Bernard（KZB）型椭圆系统上的两次穿孔环面。我们推导出椭圆KZB系统的一个显式的全重数表示为一个向量的迭代积分与一个额外的标记点，并探讨相容性条件的两套代数生成元出现在两个微分方程。
英文摘要：
Two different constructions generating the low-energy expansion of genus-one configuration-space integrals appearing in one-loop open-string amplitudes have been put forward in \rcites{Mafra:2019xms, *Mafra:2019ddf, Broedel:2019gba}. We are going to show that both approaches can be traced back to an elliptic system of Knizhnik--Zamolodchikov--Bernard(KZB) type on the twice-punctured torus. We derive an explicit all-multiplicity representation of the elliptic KZB system for a vector of iterated integrals with an extra marked point and explore compatibility conditions for the two sets of algebra generators appearing in the two differential equations.
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