  We study perturbations that break gauge symmetries in lattice gauge theories.
As a paradigmatic model, we consider the three-dimensional Abelian-Higgs (AH)
model with an N-component scalar field and a noncompact gauge field, which is
invariant under U(1) gauge and SU(N) transformations. We consider
gauge-symmetry breaking perturbations that are quadratic in the gauge field,
such as a photon mass term, and determine their effect on the critical behavior
of the gauge-invariant model, focusing mainly on the continuous transitions
associated with the charged fixed point of the AH field theory. We discuss
their relevance and compute the (gauge-dependent) exponents that parametrize
the departure from the critical behavior (continuum limit) of the
gauge-invariant model. We also address the critical behavior of lattice AH
models with broken gauge symmetry, showing an effective enlargement of the
global symmetry, from U(N) to O(2N), which reflects a peculiar cyclic
renormalization-group flow in the space of the lattice AH parameters and of the
photon mass.
