Breaking of Gauge Symmetry in Lattice Gauge Theories

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