论文标题
镜像在费米子拓扑命令中的异常
Mirror anomaly in fermionic topological orders
论文作者
论文摘要
我们研究了一般的2D费米子拓扑订单，由镜子对称性富含$ \ mathcal {m}^2 = 1 $。众所周知，某些富含费尔米金拓扑秩序（镜集）的镜像对称性是异常的，因为它们无法在严格的二维中实现，但必须生活在3D拓扑结晶超导体的表面上。镜像异常或等效的3D拓扑结晶超导体具有$ \ mathbb {z} _ {16} $分类。在这项工作中，我们为$ \ mathbb {z} _ {16} $ sirrorm primary sirrorm sermaly for Fermionic Mirror Sets提供了明显的表达，即\ emph {异常指示器}。该推导基于最近开发的折叠方法，该方法最初是针对骨器拓扑秩序提出的。我们将其推广到费米昂系统。通过这种方法，我们在表面纤维化拓扑秩和3D散装拓扑晶体超导体之间建立了直接的散装对应关系。另外，在推导过程中，我们获得了费米子拓扑秩序的一些一般特性，以及对费米子镜集特性的一些约束。
We study general 2D fermionic topological orders enriched by the mirror symmetry with $\mathcal{M}^2=1$. It is known that certain mirror symmetry enriched fermionic topological orders (mirror SETs) are anomalous, in the sense that they cannot be realized in strict two dimensions but have to live on the surface of 3D topological crystalline superconductors. Mirror anomaly, or equivalently 3D topological crystalline superconductor, has a $\mathbb{Z}_{16}$ classification. In this work, we derive an explicit expression, namely an \emph{anomaly indicator}, for the $\mathbb{Z}_{16}$ mirror anomaly for general fermionic mirror SETs. This derivation is based on the recently developed folding approach, originally proposed for bosonic topological orders. We generalize it to fermion systems. Through this approach, we establish a direct bulk-boundary correspondence between surface fermionic topological orders and 3D bulk topological crystalline superconductors. In addition, during the derivation, we obtain some general properties of fermionic topological orders as well as a few constraints on properties of fermionic mirror SETs.
