高亏格模图张量之间的恒等式

IF 1.2 3区数学 Q1 MATHEMATICS

Communications in Number Theory and Physics Pub Date : 2020-10-02 DOI:10.4310/cntp.2022.v16.n1.a2

E. D'hoker, O. Schlotterer

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引用次数: 11

摘要

高亏格模图张量将Feynman图映射到亏格-$h$紧Riemann曲面的Torelli空间上的函数，这些函数在模群$Sp（2h，\mathbb Z）$下变换为张量，从而推广了Kawazumi的一个构造。对于任意亏格和任意张量秩，证明了一个环与树级模图张量之间的代数恒等式的无穷大族。我们还导出了一个适用于高循环阶模图张量的恒等式族。

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Identities among higher genus modular graph tensors

Higher genus modular graph tensors map Feynman graphs to functions on the Torelli space of genus-$h$ compact Riemann surfaces which transform as tensors under the modular group $Sp(2h , \mathbb Z)$, thereby generalizing a construction of Kawazumi. An infinite family of algebraic identities between one-loop and tree-level modular graph tensors are proven for arbitrary genus and arbitrary tensorial rank. We also derive a family of identities that apply to modular graph tensors of higher loop order.

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来源期刊

Communications in Number Theory and Physics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.70

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： Focused on the applications of number theory in the broadest sense to theoretical physics. Offers a forum for communication among researchers in number theory and theoretical physics by publishing primarily research, review, and expository articles regarding the relationship and dynamics between the two fields.