标题： 双部分场理论的Hilbert级数 显示英文标题

标题： Hilbert Series of Bipartite Field Theories

摘要： 我们通过计算希尔伯特级数来研究双色场理论的介子模空间的代数结构。 双色场理论是一类4d N=1超对称规范理论，它们由带有边界的黎曼面上的双色图定义。 通过计算希尔伯特级数，我们能够确定这些理论的介子模空间的生成元和定义生成元关系。 此外，我们表明某些双色场理论表现出增强的全局对称性，这些对称性可以通过相应精炼希尔伯特级数的计算来识别。 作为我们研究的一部分，我们引入了两类在圆柱体上定义的一参数双色场理论，其介子模空间都是完整的交点环状卡拉比-丘3流形。 显示英文摘要

摘要： We study the algebraic structure of the mesonic moduli spaces of bipartite field theories by computing the Hilbert series. Bipartite field theories form a large family of 4d N=1 supersymmetric gauge theories that are defined by bipartite graphs on Riemann surfaces with boundaries. By calculating the Hilbert series, we are able to identify the generators and defining generator relations of the mesonic moduli spaces of these theories. Moreover, we show that certain bipartite field theories exhibit enhanced global symmetries which can be identified through the computation of the corresponding refined Hilbert series. As part of our study, we introduce two one-parameter families of bipartite field theories defined on cylinders whose mesonic moduli spaces are all complete intersection toric Calabi-Yau 3-folds.