Basis decompositions and a Mathematica package for modular graph forms
Basis decompositions and a Mathematica package for modular graph forms
复制标题
用于模块化图形形式的基础分解和 Mathematica 包
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Jan E. Gerken
中科院分区：
文献类型：
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作者：
Jan E. Gerken
模图形式（MGF）是一类非全纯模形式，它自然地出现在闭弦亏格振幅的低能展开中，引起了纯数学家的极大兴趣。MGF满足许多非平凡的代数和微分关系，这些关系在文献中得到了广泛的研究，并导致了显着的简化。在本文中，我们系统地联合收割机这些关系，以获得所有的两个和三个点的MGF的总模重量w+w 12的基础分解，从香蕉图的两个著名的身份。此外，我们研究以前已知的关系，在积分表示的MGF，导致一个新的理解全纯子图约简为Fay身份的Kronecker-Eisenstein系列和打开大门分解发散图。我们提供了一个计算机实现的数学软件包ModularGraphForms的形式，其中包括获得的基础分解的MGF的操作。
Modular graph forms (MGFs) are a class of non-holomorphic modular forms which naturally appear in the low-energy expansion of closed-string genus-one amplitudes and have generated considerable interest from pure mathematicians. MGFs satisfy numerous non-trivial algebraic- and differential relations which have been studied extensively in the literature and lead to significant simplifications. In this paper, we systematically combine these relations to obtain basis decompositions of all two- and three-point MGFs of total modular weight w+w̄⩽12 , starting from just two well-known identities for banana graphs. Furthermore, we study previously known relations in the integral representation of MGFs, leading to a new understanding of holomorphic subgraph reduction as Fay identities of Kronecker–Eisenstein series and opening the door toward decomposing divergent graphs. We provide a computer implementation for the manipulation of MGFs in the form of the Mathematica package ModularGraphForms which includes the basis decompositions obtained.
影响因子：
5.4
作者：
D’Hoker, Eric
通讯作者：
D’Hoker, Eric
Melon 模块化图函数中不存在不可约的多个 zeta 值
影响因子：
1.9
作者：
D’Hoker, Eric;Green, Michael B.
通讯作者：
Green, Michael B.