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We consider the role that gauge symmetry breaking terms play on the continuumlimit of gauge theories in three dimensions. As a paradigmatic example weconsider scalar electrodynamics in which $N_f$ complex scalar fields interactwith a U(1) gauge field. We discuss under which conditions a gauge-symmetrybreaking term destabilizes the critical behavior (continuum limit) of thegauge-invariant theory. We find that the gauge symmetry is robust attransitions at which gauge fields are not critical. At charged transitions,where gauge fields are critical, gauge symmetry is lost as soon as theperturbation is added.

Breaking the gauge symmetry in lattice gauge-invariant models