Three-dimensional lattice SU($N_c$) gauge theories with multiflavor scalar fields in the adjoint representation

TL;DR

This paper explores the phase structure of three-dimensional lattice SU(N_c) gauge theories with multiple scalar flavors in the adjoint representation, analyzing Higgs phases and phase transitions through theoretical and numerical methods.

Contribution

It provides a detailed analysis of the phase diagram and symmetry-breaking patterns in multiflavor adjoint scalar SU(N_c) gauge theories, supported by Monte Carlo simulations.

Findings

Identification of different Higgs phases and their symmetry patterns

Determination of the nature of phase transition lines

Numerical confirmation of theoretical phase diagram predictions

Abstract

We consider three-dimensional lattice SU($N_c$) gauge theories with multiflavor ($N_f>1$) scalar fields in the adjoint representation. We investigate their phase diagram, identify the different Higgs phases with their gauge-symmetry pattern, and determine the nature of the transition lines. In particular, we study the role played by the quartic scalar potential and by the gauge-group representation in determining the Higgs phases and the global and gauge symmetry-breaking patterns characterizing the different transitions. The general arguments are confirmed by numerical analyses of Monte Carlo results for two representative models that are expected to have qualitatively different phase diagrams and Higgs phases. We consider the model with $N_c = 3$, $N_f=2$ and with $N_c=2$, $N_f= 4$. This second case is interesting phenomenologically to describe some features of cuprate superconductors.