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

Phase diagram and Higgs phases of 3D lattice SU(Nc) gauge theories with multiparameter scalar potentials