We study half-BPS line operators in 3d N $$ \mathcal{N} $$ = 4 gauge theories, focusing in particular on the algebras of local operators at their junctions. It is known that there are two basic types of such line operators, distinguished by the SUSY subalgebras that they preserve; the two types can roughly be called “Wilson lines” and “vortex lines,” and are exchanged under 3d mirror symmetry. We describe a large class of vortex lines that can be characterized by basic algebraic data, and propose a mathematical scheme to compute the algebras of local operators at their junctions — including monopole operators — in terms of this data. The computation generalizes mathematical and physical definitions/analyses of the bulk Coulomb-branch chiral ring. We fully classify the junctions of half-BPS Wilson lines and of half-BPS vortex lines in abelian gauge theories with sufficient matter. We also test our computational scheme in a non-abelian quiver gauge theory, using a 3d-mirror-map of line operators from work of Assel and Gomis.

中文翻译：

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镜像对称和线算子

我们在 3d N $$ \mathcal{N} $$ = 4 规范理论中研究半 BPS 线算子，特别关注局部算子在其交界处的代数。众所周知，这种线算符有两种基本类型，以它们保留的 SUSY 子代数为特征；这两种类型大致可以称为“威尔逊线”和“涡旋线”，并且在3d镜像对称下交换。我们描述了一大类可以用基本代数数据表征的涡线，并提出了一种数学方案，根据这些数据计算局部算子在其交界处的代数 - 包括单极子算子。该计算概括了体积库仑分支手性环的数学和物理定义/分析。我们将阿贝尔规范理论中半 BPS 威尔逊线和半 BPS 涡旋线的交点完全分类为具有足够物质。我们还在非阿贝尔箭袋规范理论中测试了我们的计算方案，使用来自 Assel 和 Gomis 工作的线算子的 3d 镜像图。