In connection with Classical and quantum anomalies, I\'d like to ask for a simpl

Question

In connection with Classical and quantum anomalies, I'd like to ask for a simple explanation why some anomalies lead to valid quantum field theories while some others (happily absent in the standard model) seem to make the corresponding quantum field theory inconsistent.

Edit: More specifically, in case of an anomalous gauge symmetry: Why can't one get a valid theory by using a central extension of the gauge group as the quantum version of the gauge group? Has this been tried and not found working, giving a no-go theorem? Or would that lead to a different classical theory in the limit ??0?

Explanation / Answer

In quantum field theories it is believed that anomalies in gauge symmetries (in contrast to rigid symmetries) cannot be coped with and must be canceled at the level of the elementary fields.

May be the earliest work on the subject is: C. Bouchiat, J. Iliopoulos and P. Meyer,

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