Phase diagram and Higgs phases of three-dimensional lattice SU(Nc) gauge theories with multiparameter scalar potentials

We consider three-dimensional lattice SU(Nc) gauge theories with degenerate multicomponent (Nf>1) complex scalar fields that transform under the fundamental representation of the gauge SU(Nc) group and of the global U(Nf) invariance group, interacting with the most general quartic potential compatible with the global (flavor) and gauge (color) symmetries. We investigate the phase diagrams, identifying the low-temperature Higgs phases and their global and gauge symmetries, and the critical behaviors along the different transition lines. In particular, we address the role of the quartic scalar potential, which determines the Higgs phases and the corresponding symmetry-breaking patterns. Our study is based on the analysis of the minimum-energy configurations and on numerical Monte Carlo simulations. Moreover, we investigate whether some of the transitions observed in the lattice model can be related to the behavior of the renormalization-group flow of the continuum field theory with the same symmetries and field content around its stable charged fixed points. For Nc=2, numerical results are consistent with the existence of charged critical behaviors for Nf>Nf, with 20<40.