AI 中文总结
研究通过3d/3d对应对4d $\mathcal{N}=2$阿吉雷斯 - 道格拉斯理论进行扭曲维数约化，由4d BPS谱导出透镜空间三角剖分确定ACSM理论，探讨其流向SCFT和TQFT情况，还研究TQFT与VOA关系及相关检验，重现特定最小SCFT。
AI 中文摘要
我们通过3d/3d对应研究4d $\mathcal{N}=2$阿吉雷斯 - 道格拉斯理论的扭曲维数约化，聚焦于作为类$\mathcal{S}$理论$T[\mathcal{C}]$实现的$(A_1, A_{2n})$理论，其中曲线$\mathcal{C}$有一个不规则穿孔。我们认为得到的3d $\mathcal{N}=4$秩为0的超共形场论（SCFT）是迪莫夫特 - 盖奥托 - 古科夫（DGG）阿贝尔陈 - 西蒙斯 - 物质（ACSM）理论$T[M_3^{(k)}]$的红外不动点，该理论对应透镜空间$M_3^{(k)}=L(2n + 3,2k)$，通过将$\mathcal{C}$以扭转$k \in \mathbb{Z}_{2n + 3}^\times$纤维化在圆上得到。由4d BPS谱导出的$M_3^{(k)}$的三角剖分确定了ACSM理论及其超势。当单极子超势在精确意义下接近最大时，$T[M_3^{(k)}]$流向预期的SCFT，而最大超势给出$T_A[M_3^{(k)}]$，它直接流向非酉TQFT，即SCFT的拓扑$A$扭转。从几何上看，SCFT和TQFT点通过在三角剖分的边之间移动锥形奇点相关，我们提出奇异边和SCFT点之间的对应关系，预测SCFT何时是酉TQFT。来自$M_3^{(k)}$的TQFT可以在其全纯边界上支持二维顶点算子代数（VOA），包括$k = 1$时4d SCFT的舒尔扇区VOA。对于$n = k = 1$，我们的构造从$L(5,2)$重现了冈和山崎的最小3d $\mathcal{N}=4$ SCFT，其中$T_A[M_3^{(k)}]$是在其边界上支持$M(2,5)$的杨 - 李TQFT。我们详细检验了我们的提议，从赛弗特流形上的配分函数重建红外TQFT的模结构，并匹配相位以从ACSM数据确定VOA中心荷$c_{\text{2d}} \bmod 8$，包括引力陈 - 西蒙斯能级。
英文摘要
We study the twisted dimensional reduction of 4d $\mathcal{N}=2$ Argyres--Douglas theories via the 3d/3d correspondence, focussing on $(A_1, A_{2n})$ theories realised as the class-$\mathcal{S}$ theory $T[\mathcal{C}]$ for a curve $\mathcal{C}$ with one irregular puncture. We argue the resulting 3d $\mathcal{N}=4$ rank-0 superconformal field theory (SCFT) arises as the IR fixed point of a Dimofte--Gaiotto--Gukov (DGG) abelian Chern--Simons-matter (ACSM) theory $T[M_3^{(k)}]$ for the lens space $M_3^{(k)}=L(2n+3,2k)$, obtained by fibering $\mathcal{C}$ over the circle with twist $k \in \mathbb{Z}_{2n+3}^\times$. The triangulation of $M_3^{(k)}$, derived from the 4d BPS spectrum, determines the ACSM theory including its superpotential. $T[M_3^{(k)}]$ flows to the expected SCFT when the monopole superpotential is near-maximal in a precise sense, while the maximal superpotential gives $T_A[M_3^{(k)}]$, which flows directly to a non-unitary TQFT, the topological $A$-twist of the SCFT. Geometrically, the SCFT and TQFT points are related by shifting conical singularities between edges of the triangulation, and we propose a correspondence between singular edges and SCFT points predicting when the SCFT is a unitary TQFT. The TQFTs from $M_3^{(k)}$ can support 2d vertex operator algebras (VOAs) on their holomorphic boundary, including the Schur-sector VOA of the 4d SCFT for $k=1$. For $n=k=1$, our construction reproduces the minimal 3d $\mathcal{N}=4$ SCFT of Gang and Yamazaki from $L(5,2)$, where $T_A[M_3^{(k)}]$ is the Yang--Lee TQFT supporting $M(2,5)$ on its boundary. We check our proposals in detail, reconstructing the modular structure of the IR TQFTs from partition functions on Seifert manifolds, and matching phases to determine VOA central charges $c_{\text{2d}} \bmod 8$ from the ACSM data, including the gravitational Chern--Simons level.
Comments71 pages, 14 figures; added several references
