论文标题
Calabi-yau品种的冰锥系列和迭代的积分
The ice cone family and iterated integrals for Calabi-Yau varieties
论文作者
论文摘要
我们首次在二维中首次提供了多环相等冰锥图的完全分析结果。通过分析这些积分的主要奇异性，我们发现，可以将最大切割二维的最大切割分为同一时期的两个副本，这些副本描述了相等质量的香蕉积分的Calabi-yau品种。我们在任意数量的循环中获得了主积分的猜想基础，并以同一类的迭代积分满足的微分方程系统解决了在同一质量香蕉积分的背景下出现的相同类别的迭代积分。然后，我们继续表明，当按照模量空间的规范坐标表达时，我们的结果自然可以写成，因为它涉及卡拉比（Calabi-Yau）品种的几何不变的迭代积分。我们的结果表明，如何将纯粹功能和先验权重的概念扩展到卡拉比Yau品种的情况下。最后，我们还从同一类迭代的积分方面获得了卡拉比野品种时期的新颖表示，并且我们表明，这些时期之间众所周知的二次关系减少到这些迭代的积分之间的简单洗牌关系。
We present for the first time fully analytic results for multi-loop equal-mass ice cone graphs in two dimensions. By analysing the leading singularities of these integrals, we find that the maximal cuts in two dimensions can be organised into two copies of the same periods that describe the Calabi-Yau varieties for the equal-mass banana integrals. We obtain a conjectural basis of master integrals at an arbitrary number of loops, and we solve the system of differential equations satisfied by the master integrals in terms of the same class of iterated integrals that have appeared earlier in the context of equal-mass banana integrals. We then go on and show that, when expressed in terms of the canonical coordinate on the moduli space, our results can naturally be written as iterated integrals involving the geometrical invariants of the Calabi-Yau varieties. Our results indicate how the concept of pure functions and transcendental weight can be extended to the case of Calabi-Yau varieties. Finally, we also obtain a novel representation of the periods of the Calabi-Yau varieties in terms of the same class of iterated integrals, and we show that the well-known quadratic relations among the periods reduce to simple shuffle relations among these iterated integrals.
