We propose the general idea that 't Hooft anomalies of generalized global symmetries can be understood in terms of the properties of solitonic defects, which generically are non-topological defects. The defining property of such defects is that they act as sources for background fields of generalized symmetries. 't Hooft anomalies arise when solitonic defects are charged under these generalized symmetries. We illustrate this idea for several kinds of anomalies in various spacetime dimensions. A systematic exploration is performed in 3d for 0-form, 1-form, and 2-group symmetries, whose 't Hooft anomalies are related to two special types of solitonic defects, namely vortex line defects and monopole operators. This analysis is supplemented with detailed computations of such anomalies in a large class of 3d gauge theories. Central to this computation is the determination of the gauge and 0-form charges of a variety of monopole operators: these involve standard gauge monopole operators, but also fractional gauge monopole operators, as well as monopole operators for 0-form symmetries. The charges of these monopole operators mainly receive contributions from Chern-Simons terms and fermions in the matter content. Along the way, we interpret the vanishing of the global gauge and ABJ anomalies, which are anomalies not captured by local anomaly polynomials, as the requirement that gauge monopole operators and mixed monopole operators for 0-form and gauge symmetries have non-fractional integer charges.

中文翻译：

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孤子缺陷引起的广义对称性异常

我们提出这样的总体思想：广义全局对称性的特霍夫特异常可以用孤子缺陷的性质来理解，孤子缺陷通常是非拓扑缺陷。此类缺陷的定义属性是它们充当广义对称性背景场的来源。当孤子缺陷在这些广义对称性下带电时，就会出现“特霍夫特异常”。我们用不同时空维度的几种异常来说明这个想法。在 3d 中对 0 型、1 型和 2 群对称性进行了系统的探索，其 't Hooft 异常与两种特殊类型的孤子缺陷有关，即涡线缺陷和单极子算子。这一分析得到了对一大类 3d 规范理论中此类异常的详细计算的补充。此计算的核心是确定各种单极子算子的规范和 0 形式电荷：这些涉及标准规范单极子算子，但也包括分数规范单极子算子，以及 0 形式对称性的单极子算子。这些单极子算子的电荷主要受到物质含量中陈-西蒙斯项和费米子的贡献。在此过程中，我们将全局规范和 ABJ 异常（局部异常多项式未捕获的异常）的消失解释为 0 形式和规范对称性的规范单极算子和混合单极算子具有非分数整数电荷的要求。