论文标题
从迭代的Eisenstein积分中生成所有模块化图的系列
Generating series of all modular graph forms from iterated Eisenstein integrals
论文作者
论文摘要
我们研究生成一系列的圆环积分，这些积分包含与无质量的单环闭合弦振幅相关的所有所谓模块图形式。通过分析生成系列的微分方程，我们构建了一个解决方案，用于其低能扩展到反向字符串张力$α'$中的所有订单。我们的解决方案是通过涉及多个ZETA值的初始数据和圆环模块化参数的某些实重分析函数来表达的。这些功能是由全体形态迭代的Eisenstein积分的真实和虚构部分构建的，应与Brown最近建造的真实分析模块化形式密切相关。我们将详细研究我们的实体对象的特性，并在$α'$扩展中为固定顺序提供明确的例子。特别是，我们的解决方案允许以给定的重量计数线性独立的模块化图表，从而确认了先前的部分结果，并为迄今尚未探索的重量提供了预测。它还为$α'$扩展的统一超然性主题提供了新的启示。
We study generating series of torus integrals that contain all so-called modular graph forms relevant for massless one-loop closed-string amplitudes. By analysing the differential equation of the generating series we construct a solution for its low-energy expansion to all orders in the inverse string tension $α'$. Our solution is expressed through initial data involving multiple zeta values and certain real-analytic functions of the modular parameter of the torus. These functions are built from real and imaginary parts of holomorphic iterated Eisenstein integrals and should be closely related to Brown's recent construction of real-analytic modular forms. We study the properties of our real-analytic objects in detail and give explicit examples to a fixed order in the $α'$-expansion. In particular, our solution allows for a counting of linearly independent modular graph forms at a given weight, confirming previous partial results and giving predictions for higher, hitherto unexplored weights. It also sheds new light on the topic of uniform transcendentality of the $α'$-expansion.
