论文标题
关于广义对称性，无间隙激发，广义对称性保护拓扑状态和异常的注意事项
Note on Generalized Symmetries, Gapless Excitations, Generalized Symmetry Protected Topological states, and Anomaly
论文作者
论文摘要
我们认为许多具有广义对称性的身体系统，例如最近引入的较高形式的对称性和“张量对称性”。我们考虑了晶格汉密尔顿人的一种一般形式，该形式允许一定程度的非局部性。基于双重概括对称性的假设，我们明确构建了低能激发态。在“衡量”双重概括对称性之后，我们还为哈密顿尔顿尔顿尔顿一般的hhoft异常得出了“ hoft异常”。具有双重异常对称对称性的3D系统可以看作是具有1型对称性的4D广义对称性保护拓扑（SPT）状态的边界。我们还提出了具有混合1形式和0形式对称拓扑响应理论及其物理结构的4D SPT状态的原型示例。该SPT状态的边界可以是3D异常的QED状态，也可以是一个异常的1形对称性富含拓扑顺序。通过尺寸兼容/还原来获得见解。尺寸压实后，具有n对双1形对称对称的n对的3D系统还原为具有2 u（1）全局对称性的2n对的1D系统，这是普通2D SPT状态的边界；带有张量对称性的3D系统还原为1D Lifshitz理论，该理论受到系统质量保护的中心保护。
We consider quantum many body systems with generalized symmetries, such as the higher form symmetries introduced recently, and the "tensor symmetry". We consider a general form of lattice Hamiltonians which allow a certain level of nonlocality. Based on the assumption of dual generalized symmetries, we explicitly construct low energy excited states. We also derive the 't Hooft anomaly for the general Hamiltonians after "gauging" the dual generalized symmetries. A 3d system with dual anomalous 1-form symmetries can be viewed as the boundary of a 4d generalized symmetry protected topological (SPT) state with 1-form symmetries. We also present a prototype example of 4d SPT state with mixed 1-form and 0-form symmetry topological response theory as well as its physical construction. The boundary of this SPT state can be a 3d anomalous QED state, or an anomalous 1-form symmetry enriched topological order. Insights are gained by dimensional compatification/reduction. After dimensional compactification, the 3d system with N pairs of dual 1-form symmetries reduces to a 1d system with 2N pairs of dual U(1) global symmetries, which is the boundary of an ordinary 2d SPT state; while the 3d system with the tensor symmetry reduces to a 1d Lifshitz theory, which is protected by the center of mass conservation of the system.
