论文标题
二维费米子CFT中的拓扑缺陷线
Topological Defect Lines in Two Dimensional Fermionic CFTs
论文作者
论文摘要
我们考虑二维费米子形成式田间理论（CFTS）中的拓扑缺陷线（TDL）。除了继承TDL的所有属性外，Fermionic CFT中的TDL还可以在其端点和交界处托管费米子缺陷算子。此外，有一种新型的TDL，称为Q-Type TDL，在骨cfts中没有类似物。他们的独特特征是在TDLS的世界上生活的额外的一维主要武器。费米子CFT中TDL的属性是在超级融合类别的数学语言中捕获的。我们建议对$ \ mathbb z_8 $分类的$ \ mathbb z_2 $对称性的$ \ mathbb z_8 $分类进行分类。我们明确地为所有非平凡类别求解了F-Moves，并得出了约束缺陷算子频谱的相应旋转选择规则。我们在标准的费米子最小模型和两个例外模型中的一组TDL中找到了完整的TDL集合，这些模型为Rank-2超级融合类别提供了CFT实现。最后，我们讨论了保留Q-type TDL的重新归一化组流量的约束。
We consider topological defect lines (TDLs) in two-dimensional fermionic conformal field theories (CFTs). Besides inheriting all the properties of TDLs in bosonic CFTs, TDLs in fermionic CFTs could host fermionic defect operators at their endpoints and junctions. Furthermore, there is a new type of TDLs, called q-type TDLs, that have no analog in bosonic CFTs. Their distinguishing feature is an extra one-dimensional Majorana fermion living on the worldline of the TDLs. The properties of TDLs in fermionic CFTs are captured in the mathematical language of the super fusion category. We propose a classification of the rank-2 super fusion categories generalizing the $\mathbb Z_8$ classification for the anomalies of $\mathbb Z_2$ symmetry. We explicitly solve the F-moves for all the nontrivial categories, and derive the corresponding spin selection rules that constrain the spectrum of the defect operators. We find the full set of TDLs in the standard fermionic minimal models and a partial set of TDLs in the two exceptional models, which give CFT realizations to the rank-2 super fusion categories. Finally, we discuss a constraint on the renormalization group flow that preserves a q-type TDL.
