论文标题
线缺陷量子数和异常
Line Defect Quantum Numbers & Anomalies
论文作者
论文摘要
我们探索线缺陷的全局对称量子数与't Hooft异常之间的连接。相对于局部（点）操作员，线缺陷可能在内部和时空对称性下进行投影转换。这种现象称为对称分数，通常表示存在某些离散的hooft异常。我们在四个维度的自由麦克斯韦理论的背景下详细描述了这一点。这种理解使我们能够通过分析动力学磁性单极的分数量子数来推断出具有重新归一化组的非亚伯仪理论的hhoft异常。我们用$ SU（2）$量规理论说明了这种方法，其中物质费用在量规组的各种表示中。对于伴随物质，我们发现了涉及0形式和1形对称性的混合异常，从而扩大了先前的结果。对于带有基本费米子的$ su（2）$ qCD，麦克斯韦阶段线的分数模式编码的0形式对称的hooft异常是熟悉的扰动（三角形）异常的结果。
We explore the connection between the global symmetry quantum numbers of line defects and 't Hooft anomalies. Relative to local (point) operators, line defects may transform projectively under both internal and spacetime symmetries. This phenomenon is known as symmetry fractionalization, and in general it signals the presence of certain discrete 't Hooft anomalies. We describe this in detail in the context of free Maxwell theory in four dimensions. This understanding allows us to deduce the 't Hooft anomalies of non-Abelian gauge theories with renormalization group flows into Maxwell theory by analyzing the fractional quantum numbers of dynamical magnetic monopoles. We illustrate this method in $SU(2)$ gauge theories with matter fermions in diverse representations of the gauge group. For adjoint matter, we uncover a mixed anomaly involving the 0-form and 1-form symmetries, extending previous results. For $SU(2)$ QCD with fundamental fermions, the 't Hooft anomaly for the 0-form symmetries that is encoded by the fractionalization patterns of lines in the Maxwell phase is a consequence of the familiar perturbative (triangle) anomaly.
