发表机构
Center of Mathematical Sciences and Applications, Harvard University; Institute for Theoretical Physics, Utrecht University; Jefferson Physical Laboratory, Harvard University（哈佛大学数学科学与工程应用中心; 乌得勒支大学理论物理研究所; 哈佛大学杰斐逊物理实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在类型A类S理论中引入非阿贝尔Hodge理论，通过Hitchin系统单值数据细化退化UV曲线的渐近极限，构造装饰尖点标签，并在SL(3,C)四穿孔球面和SL(4,C)双穿孔环面上示例。
AI 中文摘要
我们在类型$A$类$\mathcal{S}$理论中发展了渐近极限的非阿贝尔Hodge理论精细化，用与Hitchin系统相关的规范理论数据丰富了退化UV曲线的几何描述。UV曲线的退化产生一个长的管道（plumbing tube），我们为其配备一个具有正则奇异对数模型的Hitchin-Simpson平坦联络的局部单值数据。单值矩阵的半单部分和幂单部分分别控制平坦截面通过管道时的幂律增长和对数增长。将此非阿贝尔和乐与几何的Picard-Lefschetz单值相结合，得到一个装饰的尖点标签，该标签包含Higgs丛信息，并逐管道扩展到边界除子的交点。对于每个管道，我们要求由固定数据和粘合数据指定的弱规范代数位于约化单值中心化子中。在类型$A$中，我们将局部单值标签组织为离散类型，由半单部分的特征空间重数和幂单部分的对数幂零Jordan型指定。最后，我们在四穿孔球面上的$SL(3,\mathbb C)$和双穿孔环面上的$SL(4,\mathbb C)$上说明该构造。
英文摘要
We develop a non-Abelian Hodge-theoretic refinement of asymptotic limits in type-$A$ class-$\mathcal S$ theories, enriching the geometric description of the degenerating UV curve with gauge-theoretic data encoded by the associated Hitchin system. A degeneration of the UV curve produces a long plumbing tube, which we equip with the local monodromy data of a Hitchin-Simpson flat connection admitting a regular-singular logarithmic model. The semisimple and unipotent parts of the monodromy govern, respectively, the power-law and logarithmic growth of flat sections through the tube. Combining this non-Abelian holonomy with the geometric Picard-Lefschetz monodromy yields a decorated cusp label that incorporates Higgs-bundle information and extends tube-wise to intersections of boundary divisors. For each tube, we require the weak gauge algebra specified by the fixture and gluing data to lie in the reductive monodromy centralizer. In type $A$, we organize the local monodromy labels into discrete types specified by the eigenspace multiplicities of the semisimple part and the Jordan type of the nilpotent logarithm of the unipotent part. Finally, we illustrate the construction for $SL(3,\mathbb C)$ on the four-punctured sphere and $SL(4,\mathbb C)$ on the two-punctured torus.
Comments54 pages, 9 figures, and 3 tables; references added
