论文标题
在（2+1）D拓扑阶段计量谎言组对称性
Gauging Lie group symmetry in (2+1)d topological phases
论文作者
论文摘要
我们提出了一个通用代数框架，用于在（2+1）d拓扑阶段衡量0形式的紧凑，连接的谎言组对称性。从Lie Group $ g $的对称分数开始，我们首先将$ G $扩展到较大的对称群体$ \ tilde {g} $，因此，在拓扑阶段，与$ \ tilde {g} $有关，在拓扑阶段没有分数，并与$ \ tilde a $ a $ n $ $ n $ Chern-Simons理论。为了恢复所需的量规对称性，然后必须衡量适当的单一形式对称性（或凝结某些Abelian Anyons）才能获得最终结果。研究测量程序的一致性会导致对称分数模式与霍尔电导率之间的兼容条件。当无法始终如一地完成测量值（即无法满足兼容性条件）时，与分数化模式的对称$ g $具有't Hooft异常现象，并且我们提出了一种确定异常的（3+1）d拓扑术语的一般方法。我们提供了许多示例，包括投射简单的谎言组和统一团体来说明我们的方法。
We present a general algebraic framework for gauging a 0-form compact, connected Lie group symmetry in (2+1)d topological phases. Starting from a symmetry fractionalization pattern of the Lie group $G$, we first extend $G$ to a larger symmetry group $\tilde{G}$, such that there is no fractionalization with respect to $\tilde{G}$ in the topological phase, and the effect of gauging $\tilde{G}$ is to tensor the original theory with a $\tilde{G}$ Chern-Simons theory. To restore the desired gauge symmetry, one then has to gauge an appropriate one-form symmetry (or, condensing certain Abelian anyons) to obtain the final result. Studying the consistency of the gauging procedure leads to compatibility conditions between the symmetry fractionalization pattern and the Hall conductance. When the gauging can not be consistently done (i.e. the compatibility conditions can not be satisfied), the symmetry $G$ with the fractionalization pattern has an 't Hooft anomaly and we present a general method to determine the (3+1)d topological term for the anomaly. We provide many examples, including projective simple Lie groups and unitary groups to illustrate our approach.
