论文标题
较高属模块化图张子之间的身份
Identities among higher genus modular graph tensors
论文作者
论文摘要
较高的属模块化图张量图Feynman图将功能绘制到属属属-H $紧凑的Riemann表面上的函数，这些表面会随着模块组$ sp（2H，\ Mathbb Z）的张量而变化，从而概括了Kawazumi的构造。一环和树级模块化图张量之间的代数身份的无限家族被证明是任意属和任意张力等级的。我们还得出了一个适用于较高循环顺序的模块化图张量的身份家族。
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.
