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The only possible way Bosons admit anomalies in flat space (analogous to the case for fermions you have mentioned) is when they do not admit a covariant lagrangian. These are called by a special name, "Chiral Bosons". The usual Bose lagrangian can always be regulated to give an action free of anomalies. See section 8 of this paper. ...


If symmetry conserves some important properties of theory (like unitarity) then its explicit breaking makes theory inconsistent. For example, all gauge symmetries must be unbroken due to unitarity of theory. When they become explicitly broken, unphysical states with indefinite metric in Hilbert space arise, and unitarity is lost. That's why we worry about ...

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