论文标题
（椭圆形）模块化族家族之间的代数身份
Algebraic identities between families of (elliptic) modular graphs
论文作者
论文摘要
考虑椭圆形的模块化图之间的代数身份，其中在固定位置有几个顶点（因此是不整合），而其他位置则集成在环形世界上。在任何不整合的顶点，我们都可以粘合一个任意表达，该表达涉及椭圆形的模块图，该图形具有相同的未整合顶点。整合该顶点，我们获得了椭圆形模块图之间的新代数身份。因此，将原始的“种子”身份与其他图相结合的基本过程产生了无限数量的新身份。我们考虑了各种种子身份，其中两个顶点是不整合的。我们将它们与椭圆形模块化图的家属相连，我们获得了新的身份。每个身份都通过图表中的任意数量的链接以及不整合的顶点的位置进行了参数。在识别不整合的顶点时，这导致了涉及模块化图的代数身份，其中所有顶点都集成在世界文上。
Consider an algebraic identity between elliptic modular graphs where several vertices are at fixed locations (and hence unintegrated) while the others are integrated over the toroidal worldsheet. At any unintegrated vertex, we can glue an arbitrary expression involving elliptic modular graphs which has the same unintegrated vertex. Integrating over that vertex, we obtain new algebraic identities between elliptic modular graphs. Hence this elementary process of convoluting the original "seed" identity with other graphs yields infinite number of new identities. We consider various seed identities in which two of the vertices are unintegrated. Convoluting them with families of elliptic modular graphs, we obtain new identities. Each identity is parametrized by an arbitrary number of links in the graphs as well as the positions of unintegrated vertices. On identifying the unintegrated vertices, this leads to an algebraic identity involving modular graphs where all the vertices are integrated over the worldsheet.
