Identities between modular graph forms
Identities between modular graph forms
复制标题
模块化图形形式之间的恒等式
DOI：
10.1016/j.jnt.2017.11.015
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发表时间：
2016
影响因子：
0.7
通讯作者：
M. Green
中科院分区：
文献类型：
--
作者：
E. D'hoker;M. Green
本文研究了模块图形式之间的关系，这是在早期的论文中引入的模块图功能的推广，动机是低能量扩展的genus-one II型超弦振幅的结构。这些模图形式是与世界片环面上的装饰费曼图相关联的多重和。标准微分算子在这些模图形式上的作用允许在装饰上的代数表示。利用一阶微分算子将一般非全纯模图函数映射到全纯模形式。这个地图是用来提供证明的身份之间的模块图功能的重量小于6在早期的工作中，通过映射这些身份之间的关系，全纯模形式证明了全纯方法。该映射进一步用于展示任意权重的身份的结构。
This paper investigates the relations between modular graph forms, which are generalizations of the modular graph functions that were introduced in earlier papers motivated by the structure of the low energy expansion of genus-one Type II superstring amplitudes. These modular graph forms are multiple sums associated with decorated Feynman graphs on the world-sheet torus. The action of standard differential operators on these modular graph forms admits an algebraic representation on the decorations. First order differential operators are used to map general non-holomorphic modular graph functions to holomorphic modular forms. This map is used to provide proofs of the identities between modular graph functions for weight less than six conjectured in earlier work, by mapping these identities to relations between holomorphic modular forms which are proven by holomorphic methods. The map is further used to exhibit the structure of identities at arbitrary weight.