Symmetry-enriched quantum spin liquids in (3 + 1)d
Symmetry-enriched quantum spin liquids in (3 + 1)d
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DOI：
10.1007/jhep09(2020)022
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发表时间：
2019-04
影响因子：
5.4
通讯作者：
Po-Shen Hsin;Alex Turzillo
中科院分区：
文献类型：
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作者：
Po-Shen Hsin;Alex Turzillo
我们利用（3+ 1）d玻色场论固有的一种形式和两种形式的整体对称性来分类由普通（0-形式）整体对称性所丰富的量子相。不同的富氢相对应于不同的耦合方式的理论的背景规范场的普通对称性。分类的输入是高阶形式的对称性和0-形式对称性在理论的线和曲面上的置换作用。从这些数据中，我们分类的耦合到背景规范场的0-形式的对称性缺陷构造的更高形式的对称性缺陷。对于平凡的两种形式的对称性的分类与（2+ 1）d中的对称分解的分类相一致。我们还提供了一个系统的方法来获得对称性保护的拓扑相位，可以被吸收的耦合，我们给出了不同的耦合的相对t Hooft异常。我们讨论了几个例子，包括无隙纯U（1）规范理论和有隙阿贝尔有限群规范理论。作为应用，我们发现了具有两个伴随Weyl费米子的SU（2）规范理论在（3+ 1）d中的一个具有约束对偶的张力.
We use the intrinsic one-form and two-form global symmetries of (3+ 1) d bosonic field theories to classify quantum phases enriched by ordinary (0-form) global symmetry. Different symmetry-enriched phases correspond to different ways of coupling the theory to the background gauge field of the ordinary symmetry. The input of the classification is the higher-form symmetries and a permutation action of the 0-form symmetry on the lines and surfaces of the theory. From these data we classify the couplings to the background gauge field by the 0-form symmetry defects constructed from the higher-form symmetry defects. For trivial two-form symmetry the classification coincides with the classification for symmetry fractionalizations in (2+ 1) d. We also provide a systematic method to obtain the symmetry protected topological phases that can be absorbed by the coupling, and we give the relative’t Hooft anomaly for different couplings. We discuss several examples including the gapless pure U (1) gauge theory and the gapped Abelian finite group gauge theory. As an application, we discover a tension with a conjectured duality in (3+ 1) d for SU (2) gauge theory with two adjoint Weyl fermions.