There are a number of limitations to the theorem. In particular, spontaneous symmetry breaking of a gauge symmetry is allowed in a system with infinite spatial dimensions or a symmetry with an infinite number of variables, since in these cases there are infinite energy barriers between gauge related configurations. The theorem also does not apply to residual gauge degrees of freedom nor large gauge transformations, which can in principle be spontaneously broken. Furthermore, all current proofs rely on a lattice field theory formulation so they may be invalid in a genuine continuum field theory. It is therefore in principle plausible that there may exist exotic continuum theories for which gauge symmetries can be spontaneously broken, although such a scenario remains unlikely due to the absence of any known examples.