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

Abstract

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 < Nf* < 40.

18 pages

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• Multicomponent gauge-Higgs models with discrete Abelian gauge groups
• Non-compact lattice Higgs model with Abelian discrete gauge groups: phase diagram and gauge symmetry enlargement
• Chiral critical behavior of 3D lattice fermionic models with quartic interactions
• Charged critical behavior and nonperturbative continuum limit of three-dimensional lattice SU($N_c$) gauge Higgs models
• Color-flavor reflection in the continuum limit of two-dimensional lattice gauge theories with scalar fields
• O(5) multicriticality in the 3D two flavor SU(2) lattice gauge Higgs model