模图函数之间关系的证明
Proving relations between modular graph functions
摘要：
我们考虑在第二类弦论中四个引力子振幅的低能展开中出现的模图函数。这些图的顶点是顶点算子在环面世界表上的插入位置，而链接是连接顶点的标量格林函数。具有四个和五个链环的图满足几个非平凡关系，这些关系最近已被证明。利用格林函数的初等性质和图的细节证明了这些关系。我们还证明了与六个链接的模块图函数之间的关系。
英文摘要：
We consider modular graph functions that arise in the low energy expansion of the four graviton amplitude in type II string theory. The vertices of these graphs are the positions of insertions of vertex operators on the toroidal worldsheet, while the links are the scalar Green functions connecting the vertices. Graphs with four and five links satisfy several non--trivial relations, which have been proved recently. We prove these relations by using elementary properties of Green functions and the details of the graphs. We also prove a relation between modular graph functions with six links.
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