标题： 线缺陷半指标的$SU(N)$陈-西蒙斯理论 显示英文标题

标题： Line defect half-indices of $SU(N)$ Chern-Simons theories

摘要： 我们研究了具有规范场Neumann边界条件的3d$\mathcal{N}=2$超对称$SU(N)$Chern-Simons理论在等级$k\le -N$下的Wilson线缺陷半指标，同时包括2d费米多重态和基本3d旋波多重态以消除规范异常。 我们得出了某些精确结果，并基于$q$系列的展开提出了某些猜想。 我们发现了一些与文献中已知特殊函数的有趣联系，包括Rogers-Ramanujan函数，我们对它们提出了积分表示的猜想，以及某些Wilson线半指标广义配分函数中出现的Appell-Lerch求和，这些揭示了拟模函数的意外出现。 我们还发现了与半指标相关的 intriguing$q$差分方程，将半指标与Wilson线半指标联系起来。 其中一些结果也可以用对偶理论中的描述，该理论中对偶理论的矢量多重态具有Dirichlet边界条件。 显示英文摘要

摘要： We study the Wilson line defect half-indices of 3d $\mathcal{N}=2$ supersymmetric $SU(N)$ Chern-Simons theories of level $k\le -N$ with Neumann boundary conditions for the gauge fields, together with 2d Fermi multiplets and fundamental 3d chiral multiplets to cancel the gauge anomaly. We derive some exact results and also make some conjectures based on expansions of the $q$-series. We find several interesting connections with special functions known in the literature, including Rogers-Ramanujan functions for which we conjecture integral representations, and the appearance of Appell-Lerch sums for certain Wilson line half-index grand canonical ensembles which reveal an unexpected appearance of mock modular functions. We also find intriguing $q$-difference equations relating half-indices to Wilson line half-indices. Some of these results also have a description in terms of a dual theory with Dirichlet boundary conditions for the vector multiplet in the dual theory.