Holomorphic subgraph reduction of higher-point modular graph forms
Holomorphic subgraph reduction of higher-point modular graph forms
复制标题
高点模块化图形式的全纯子图约简
DOI：
10.1007/jhep01(2019)131
复制
发表时间：
2018
影响因子：
5.4
通讯作者：
J. Kaidi
中科院分区：
文献类型：
--
作者：
Jan E. Gerken;J. Kaidi
模图形式是一类模协变函数，它对闭弦散射振幅的低能展开有亏格一贡献。具有全纯子图的模图形式具有简化性质，即它们可以简化为具有严格较低圈阶的模图形式的乘积和。在二面角模图形式的特殊情况下，D'Hoker和绿色以前得到了这种全纯子图约化的封闭形式表达式。在目前的工作中，我们将这些结果推广到三面体模图形式。这样做涉及到确定一个模块化的协变正则化计划的某些条件收敛和离散动量，与一些元素的总和被排除在外。适当的正则化方案确定为任何数量的排除，这在原则上允许一个执行全纯子图约简的高阶模块化图形式与任意全纯子图。
A bstractModular graph forms are a class of modular covariant functions which appear in the genus-one contribution to the low-energy expansion of closed string scattering amplitudes. Modular graph forms with holomorphic subgraphs enjoy the simplifying property that they may be reduced to sums of products of modular graph forms of strictly lower loop order. In the particular case of dihedral modular graph forms, a closed form expression for this holomorphic subgraph reduction was obtained previously by D’Hoker and Green. In the current work, we extend these results to trihedral modular graph forms. Doing so involves the identification of a modular covariant regularization scheme for certain conditionally convergent sums over discrete momenta, with some elements of the sum being excluded. The appropriate regularization scheme is identified for any number of exclusions, which in principle allows one to perform holomorphic subgraph reduction of higher-point modular graph forms with arbitrary holomorphic subgraphs.