论文标题
高环日出积分的符号和共同
A Symbol and Coaction for Higher-Loop Sunrise Integrals
论文作者
论文摘要
我们为$ l $ - 环日出积分构建一个符号和雕像，包括相等质量和通用质量案例。这些构成了涉及卡拉比（Calabi-Yau）三倍及更高的积分的符号和共同体的第一个具体例子。为了实现有限长度的象征，我们以单位差分方程的形式重塑了该拓扑的主积分所满足的微分方程。我们通过包括最大切割的比率$τ_i$来增强主积分的基础。我们讨论了该结构与多种多组载体和椭圆形多个小聚集体的符号和共同体的构建的关系，特别是它与先验重量的概念的联系。
We construct a symbol and coaction for $l$-loop sunrise integrals, both for the equal-mass and generic-mass cases. These constitute the first concrete examples of symbols and coactions for integrals involving Calabi-Yau threefolds and higher. In order to achieve a symbol of finite length, we recast the differential equations satisfied by the master integrals of this topology in the form of a unipotent differential equation. We augment the basis of master integrals in a natural way by including ratios of maximal cuts $τ_i$. We discuss the relationship of this construction to constructions of symbols and coactions for multiple polylogarithms and elliptic multiple polylogarithms, in particular its connection to notions of transcendental weight.
