Gauge symmetry and symmetry breaking

[touqra]

How would one know in general, whether an original gauge symmetry in the theory is still gauge symmetrical after symmetry breaking? I mean is there a theorem or something like that?
And the other way around, is there a general way of knowing whether there is the possibility of a hidden, i.e. not manifest gauge symmetry from a theory?

 

[Haelfix]

Yes the gauge symmetry is still there in the full theory, its just not manifest anymore b/c the perturbative solution has broken the original symmetry down to a subgroup.

From the point of view of effective field theory with some set cutoffs, its no longer relevant.

The only way a gauge symmetry can disappear in quantum field theory, is if there is an anomaly present. Those sorts of theories are generally believed to be inconsistent.

 

[touqra]

Yes the gauge symmetry is still there in the full theory, its just not manifest anymore b/c the perturbative solution has broken the original symmetry down to a subgroup.

From the point of view of effective field theory with some set cutoffs, its no longer relevant.

The only way a gauge symmetry can disappear in quantum field theory, is if there is an anomaly present. Those sorts of theories are generally believed to be inconsistent.

That's what I was thinking. I was doing scalar electrodynamics after symmetry breaking, adding the ghost term and the $$R_{\xi}$$ gauge, computing the one-loop correction to the effective potential.

The question asked to show that to one-loop correction, the effective potential does not depend on $$\xi$$. But my corrections failed to cancel half of the terms with $$\xi$$.
That's how this question I posted came into my mind. Perhaps the question was wrong, and indeed the gauge symmetry is no longer manifest after symmetry breaking. Hence, it does depend on $$\xi$$.