外自同构异常
Outer Automorphism Anomalies
摘要：
我们讨论了基于经典群的规范理论中与外自同构相关的异常，即$SU(N)$的电荷共轭和$SO(2r)$的宇称。我们强调$SU(2k)$、$SO(2r)$和$E_6$对称性的电荷共轭的两个版本之间的不等价性（但通过味变换相关）。与外自同构交换的子群被确定。一些电荷共轭可能会导致悖论，通过观察到它们是异常的，因此不是对称的，可以解决这个问题。然后，我们讨论异常匹配条件，涉及的电荷共轭或宇称。有趣的例子中给出的电荷共轭是自发打破。
英文摘要：
We discuss anomalies associated with outer automorphisms in gauge theories based on classical groups, namely charge conjugations for $SU(N)$ and parities for $SO(2r)$. We emphasize the inequivalence (yet related by a flavor transformation) between two versions of charge conjugation for $SU(2k)$, $SO(2r)$, and $E_6$ symmetries. The subgroups that commute with the outer automorphisms are identified. Some charge conjugations can lead to a paradox, which is resolved by the observation that they are anomalous and hence not symmetries. We then discuss anomaly matching conditions that involve the charge conjugations or parities. Interesting examples are given where the charge conjugation is spontaneously broken.
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