论文标题
相对理论中的相对缺陷：在S类中捕获的更高形式的对称性和不规则穿刺
Relative Defects in Relative Theories: Trapped Higher-Form Symmetries and Irregular Punctures in Class S
论文作者
论文摘要
相对理论是高维拓扑量子场理论（TQFT）的边界条件，并且携带一个非平凡的缺陷组，该缺陷群是由相互非本地缺陷形成的，这些缺陷属于相对理论中。素数为6d n =（2,0）的理论是7D TQFT的边界条件，缺陷组由表面缺陷引起。在本文中，我们研究了6D n =（2,0）理论中的Codimension-两次缺陷，并发现生活在这些condimension-two中的线缺陷是相互非本地的，因此也形成了一个缺陷组。因此，6D n =（2,0）理论中的三个缺陷是相对理论内的相对缺陷。这些相对缺陷为7D散装TQFT的拓扑缺陷提供了边界条件。当在4D n = 2类S级理论构造时，带有非平整缺陷组的Codimension-2缺陷作为一种不规则的穿刺。与这种不规则穿刺相关的缺陷组为所得类S理论的1型对称性提供了额外的“被困”贡献。我们确定与大类保形和非符号不规则穿刺相关的缺陷组。一路上，我们发现了许多新的不规则穿刺类。在缺陷组的分析中，关键作用是通过对IIB字符串理论的两种几何描述来扮演的：一种由Calabi-yau三倍的孤立的高表面奇异性提供的，另一种是由单颗粒的啤酒振动提供的。
A relative theory is a boundary condition of a higher-dimensional topological quantum field theory (TQFT), and carries a non-trivial defect group formed by mutually non-local defects living in the relative theory. Prime examples are 6d N=(2,0) theories that are boundary conditions of 7d TQFTs, with the defect group arising from surface defects. In this paper, we study codimension-two defects in 6d N=(2,0) theories, and find that the line defects living inside these codimension-two defects are mutually non-local and hence also form a defect group. Thus, codimension-two defects in a 6d N=(2,0) theory are relative defects living inside a relative theory. These relative defects provide boundary conditions for topological defects of the 7d bulk TQFT. A codimension-two defect carrying a non-trivial defect group acts as an irregular puncture when used in the construction of 4d N=2 Class S theories. The defect group associated to such an irregular puncture provides extra "trapped" contributions to the 1-form symmetries of the resulting Class S theories. We determine the defect groups associated to large classes of both conformal and non-conformal irregular punctures. Along the way, we discover many new classes of irregular punctures. A key role in the analysis of defect groups is played by two different geometric descriptions of the punctures in Type IIB string theory: one provided by isolated hypersurface singularities in Calabi-Yau threefolds, and the other provided by ALE fibrations with monodromies.
