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.

中文翻译：

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较高属模图张量之间的同一性

更高的属模图张量将费曼图映射到属 -$h$ 紧黎曼曲面的 Torelli 空间上的函数，这些函数变换为模群 $Sp(2h, \mathbb{Z})$ 下的张量，从而推广 Kawazumi 的构造. 单环和树级模图张量之间的无限代数恒族被证明可用于任意属和任意张量秩。我们还推导出了一组恒等式，这些恒等式适用于更高循环阶的模图张量。