Discrete gauge anomalies revisited
Discrete gauge anomalies revisited
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发表时间：
2018-08
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通讯作者：
Chang-Tse Hsieh
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作者：
Chang-Tse Hsieh
我们重新审视了3+1维的手性费米子理论中的离散规范异常。我们重点讨论了费米子的全对称群为$\ mathm {Spin}(4)\乘以\mathbb{Z}_n$或$(\ mathm {Spin}(4)\乘以\mathbb{Z}_{2m})/\mathbb{Z}_{2}$，其中$\mathbb{Z}_2$是对角线子群$\mathbb{Z}_2$。这些异常是由一致性条件决定的——基于Dai-Freed定理——在一个与上述对称群中的任何一个相关的结构的一般时空流形上形成手性费米子理论，并由一些有限阿贝尔群的元素表示。据此，我们给出了异常抵消条件的重新表述，并将其与Ibanez和Ross先前的结果进行了比较。以形式化的方式阐明了对称扩展在离散对称异常中的作用。我们还研究了具有反常全局$\mathbb{Z}_n$对称性的费米子的间隙态，并给出了在弱耦合框架下构造这些状态的模型。
We revisit discrete gauge anomalies in chiral fermion theories in $3+1$ dimensions. We focus on the case that the full symmetry group of fermions is $\mathrm{Spin}(4)\times\mathbb{Z}_n$ or $(\mathrm{Spin}(4)\times\mathbb{Z}_{2m})/\mathbb{Z}_{2}$ with $\mathbb{Z}_2$ being the diagonal $\mathbb{Z}_2$ subgroup. The anomalies are determined by the consistency condition --- based on the Dai-Freed theorem --- of formulating a chiral fermion theory on a generic spacetime manifold with a structure associated with either one of the above symmetry groups and are represented by elements of some finite abelian groups. Accordingly, we give a reformulation of the anomaly cancellation conditions, and compare them with the previous result by Ibanez and Ross. The role of symmetry extensions in discrete symmetry anomalies is clarified in a formal fashion. We also study gapped states of fermion with an anomalous global $\mathbb{Z}_n$ symmetry, and present a model for constructing these states in the framework of weak coupling.