构造 $A$ 型好箭图单极子公式：基于箭图杨代数
Constructing the Monopole Formula for $A$-Type Good Quivers via Quiver Yangians
- Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）
- School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文利用箭图杨代数与Coulomb分支代数对应，通过边界适配生成元和Casimir关系，重构了$T_\rho(SU(N))$理论的单极子公式为截断移位箭图杨代数的Hilbert级数。
AI中文摘要：
基于箭图杨代数与Coulomb分支代数对应的猜想（该猜想已在树型箭图中得到验证），我们给出了三维 $\mathcal N=4$ 好 $A$ 型箭图规范理论（即 $T_\rho(SU(N))$ 理论）中单极子公式的箭图杨代数解释。利用代数在 $\frac12$-BPS 涡旋上的作用，我们将截断移位箭图杨代数的生成元重组为边界适配生成元，并在 Slodowy 切片 $\mathcal S^{\mathfrak{gl}_N}_\rho$ 上以 $U(N)$ Casimir 算子形式获得经典关系，该切片的坐标由这些边界适配生成元给出。我们还证明了边界适配生成元及 Casimir 关系具有正确的 fugacity，与 $T_\rho(SU(N))$ 单极子公式的 Hall-Littlewood 表达式预测一致，从而将其重构为截断移位箭图杨代数的 Hilbert 级数。
英文摘要：
Based on the conjectured (and checked for tree-type quivers) quiver Yangian/Coulomb branch algebra correspondence, we give a quiver Yangian interpretation of the monopole formulas for 3D $\mathcal N=4$ good $A$-type quiver gauge theories, also known as the $T_ρ(SU(N))$ theories. Using the algebra action on the $\frac12$-BPS vortices, we reorganize the generators of the truncated shifted quiver Yangian into boundary-adapted generators, and obtain the classical relations in terms of $U(N)$ Casimirs on the Slodowy slice $\mathcal S^{\mathfrak{gl}_N}_ρ$, whose coordinates are given by these boundary-adapted generators. We also show that the boundary-adapted generators and the Casimir relations have the correct fugacities as predicted by the Hall-Littlewood expression of the monopole formula for $T_ρ(SU(N))$, hence reconstructing it as the Hilbert series of the truncated shifted quiver Yangian.
