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    $\begingroup$ you seem to be confusing SSB for a gauge symmetry vs SSB for a flavor symmetry. these are radically different phenomena (even if conflated in the literature, perhaps more often in the cond-mat world). hopefully this will help a bit: physics.stackexchange.com/q/800131/84967 $\endgroup$
    – AccidentalFourierTransform
    Commented Jun 28 at 16:09
  • $\begingroup$ I understand this distinction, and in fact the exact puzzle for me here is that when no gauge field and thus no gauge invariance is present, such as a BCS superconductor left alone, why there are no Goldstones. Or rather why the condclusion of the absence of gapless modes on their spectrum drawn from using Anderson-Higgs mechanism still applies. $\endgroup$
    – cx1114
    Commented yesterday