发表机构
Massachusetts Institute of Technology（麻省理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文澄清了拓扑激发统计特性与对称性反常之间的关系，指出跳跃算子的对称性（与对称变换对易）是更稳健的对应基础，并通过高一维 DW 规范场耦合和规范化视角提供了统一解释。
AI 中文摘要
广义对称性和拓扑激发，以及对称性反常和拓扑激发的统计特性，被广泛认为彼此相关。然而，在建立这种关系的方式上存在陷阱。将对称性变换的晶格截断到有限区域，会得到一个对称性补丁算子，该算子在其边界处产生对称性缺陷。这种几何图像类似于一个跳跃算子在其支撑边界处产生拓扑激发，但并不提供明确的统计特性，更不用说保证与对称性反常一致。更自然且更稳健的关系是拓扑激发的跳跃算子是对称的：它们与对称性变换对易。在适当假设下，该条件在统计特性和反常之间产生一一对应关系。我们进一步将边界物质耦合到高一维度的 DW 规范场，以从规范化的角度解释这种关系。跳跃算子本质上是在规范化后作用于物理自由度的规范不变算子。一旦规范场背景固定，全局对称性来自保持该背景的规范变换，而跳跃的对称条件正是剩余的规范不变性。这一区分澄清了文献中潜在的误解，并为比较对称性和拓扑激发提供了更可靠的框架。
英文摘要
Generalized symmetries and topological excitations, as well as symmetry anomalies and the statistics of topological excitations, are widely believed to be related. There are, however, pitfalls in how this relation is established. A lattice truncation of a symmetry transformation to a finite patch gives a symmetry patch operator that creates symmetry defects at its boundary. This geometric picture resembles a hopping operator creating topological excitations at the boundary of its support, but does not provide well-defined statistics, let alone guarantee agreement with the symmetry anomaly. A more natural and robust relation is that the hopping operators of topological excitations are symmetric: they commute with symmetry transformations. Under suitable assumptions, this condition yields a one-to-one correspondence between statistics and anomalies. We further couple boundary matter to a DW gauge field in one higher dimension to explain this relation from the perspective of gauging. A hopping operator is, in essence, a gauge-invariant operator acting on the physical degrees of freedom after gauging. Once the gauge-field background is fixed, global symmetry comes from gauge transformations that preserve that background, while the symmetric condition on hopping is precisely the remaining gauge invariance. This distinction clarifies potential misconceptions in the literature and provides a more reliable framework for comparing symmetries and topological excitations.
Comments56 pages
