标题： 三环香蕉积分的模形式 显示英文标题

标题： Modular forms for three-loop banana integrals

摘要： 我们研究多参数K3曲面族的周期，这些周期对于计算某些类费曼积分的最大切割是相关的。 我们关注它们的自守性质，并且我们证明一般来说，周期定义了正交模形式。 利用小秩李群之间的例外同构，我们展示了如何通过周期上的交积来识别其周期可以用其他在数学文献中已被研究的模形式类来表示的K3曲面。 我们将我们的结果应用于三环香蕉积分的最大切割，并且我们证明根据质量配置的不同，最大切割定义了普通模形式或赫尔德、西格尔或厄米特模形式。 显示英文摘要

摘要： We study periods of multi-parameter families of K3 surfaces, which are relevant to compute the maximal cuts of certain classes of Feynman integrals. We focus on their automorphic properties, and we show that generically the periods define orthogonal modular forms. Using exceptional isomorphisms between Lie groups of small rank, we show how one can use the intersection product on the periods to identify K3 surfaces whose periods can be expressed in terms of other classes of modular forms that have been studied in the mathematics literature. We apply our results to maximal cuts of three-loop banana integrals, and we show that depending on the mass configuration, the maximal cuts define ordinary modular forms or Hilbert, Siegel or hermitian modular forms.