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This question is a continuation of the answer posted for this question about anomalies.

Is there a violation of the Ward identity associated with an anomalous global symmetry? If yes, why is the cancellation of global anomaly not as important as the cancellation of local anomalies for a gauge symmetry to maintain the consistency of a theory?

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Of course an anomalous global symmetry destroys the associated Ward identity, but...we don't care so much about that. The Ward identity of global symmetries is not needed for consistency of the theory. However, a broken local Ward identity completely destroys the associated gauge theory, in particular since the decoupling of the unphysical degrees of freedom relies on the Ward identity.

For a much more elaborate discussion of why an anomalous gauge symmetry is really bad, see this answer.

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