Outer Automorphism Anomalies

Kavli Affiliate: Tom Melia

| First 5 Authors: Brian Henning, Xiaochuan Lu, Tom Melia, Hitoshi Murayama,

| Summary:

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 between two versions of charge
conjugation for $SU(N)$ symmetries, and also two versions of parity for
$SO(2r)$ 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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