论文标题
非阿布尔有限群的异常，通过COBORDISM
Anomalies of non-Abelian finite groups via cobordism
论文作者
论文摘要
我们使用COBORDISM理论来分析4个时空维度中有限非亚伯对称性的异常。通过应用“异常相互作用”的方法，该方法利用$η$ invariant的函数和自然性，将异常的异常与其他（有限或紧凑型谎言）组的异常相关联，我们在许多示例中都在许多示例中得出许多示例，包括$ s_3 $ a $ a $ a $ a $ a $ a $ a $ a444。 $ \ mathrm {sl}（2，\ mathbb {f} _3）$。对于有限的阿贝尔群体，众所周知，通过组扩展，可以以对低能物理学没有影响的方式“截断”。我们将这个想法扩展到非亚伯式的对称性。例如，我们证明一个具有$ A_4 $对称性的系统可以使异常无异常，只有三分之一的费米斯通过传递给更大的对称性。作为另一个例子，我们发现使用$ \ mathrm {sl}（2，\ mathbb {f} _3 _3）$对称性的一种众所周知的夸克和轻顿群众模型是异常的，但是可以通过将对称性扩大到$ \ mathbb {z z}/3 $ extermension of Symortry来取消$ \ mathrm {sl}（2，\ mathbb {f} _3）$。
We use cobordism theory to analyse anomalies of finite non-abelian symmetries in 4 spacetime dimensions. By applying the method of `anomaly interplay', which uses functoriality of cobordism and naturality of the $η$-invariant to relate anomalies in a group of interest to anomalies in other (finite or compact Lie) groups, we derive the anomaly for every representation in many examples motivated by flavour physics, including $S_3$, $A_4$, $Q_8$, and $\mathrm{SL}(2,\mathbb{F}_3)$. In the case of finite abelian groups, it is well known that anomalies can be `truncated' in a way that has no effect on low-energy physics, by means of a group extension. We extend this idea to non-abelian symmetries. We show, for example, that a system with $A_4$ symmetry can be rendered anomaly-free, with only one-third as many fermions as naïvely required, by passing to a larger symmetry. As another example, we find that a well-known model of quark and lepton masses utilising the $\mathrm{SL}(2,\mathbb{F}_3)$ symmetry is anomalous, but that the anomaly can be cancelled by enlarging the symmetry to a $\mathbb{Z}/3$ extension of $\mathrm{SL}(2,\mathbb{F}_3)$.
