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I often see discussion about "saturating" an anomaly in papers having to do with things discrete 't Hooft anomalies, anomaly inflow, and so on. An example (there are many other papers) is from the abstract of arXiv:1706.05731

We show that the domain-wall carries a 't Hooft anomaly in this case. The anomaly can be saturated by, e.g., charge-conjugation breaking on the wall or by the domain wall theory becoming gapless (a gapless model that saturates the anomaly is SU(2)1 WZW).

Is this usage a synonym for "matching" a 't Hooft anomaly, or is there something more to it?

I think I understand how a low energy effective theory must have the same 't Hooft anomaly when coupled to a background gauge field as the UV theory, but I think I am missing something about how spontaneous symmetry breaking fits into all of this, so I am looking for some clarification.

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    $\begingroup$ Prima facie, it is a synonym for "suitable matching", in a recondite setting, which I find as exotic as you might do. SSB is relevant in that its Goldstone bosons replicate/match good (global) anomalies through topological WZW terms... $\endgroup$
    – Cosmas Zachos
    Commented May 29, 2023 at 20:01

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