Charged critical behavior and nonperturbative continuum limit of three-dimensional lattice SU($N_c$) gauge Higgs models

Abstract: We consider the three-dimensional (3D) lattice SU($N_c$) gauge Higgs theories with multicomponent ($N_f>1$) degenerate scalar fields and U($N_f$) global symmetry, focusing on systems with $N_c=2$, to identify critical behaviors that can be effectively described by the corresponding 3D SU($N_c$) gauge Higgs field theory. The field-theoretical analysis of the RG flow allows one to identify a stable charged fixed point for large values of $N_f$, that would control transitions characterized by the global symmetry-breaking pattern ${\rm U}(N_f)\rightarrow \mathrm{SU}(2)\otimes \mathrm{U}(N_f-2)$. Continuous transitions with the same symmetry-breaking pattern are observed in the SU(2) lattice gauge model for $N_f \ge 30$. Here we present a detailed finite-size scaling analysis of the Monte Carlo data for several large values of $N_f$. The results are in substantial agreement with the field-theoretical predictions obtained in the large-$N_f$ limit. This provides evidence that the SU($N_c$) gauge Higgs field theories provide the correct effective description of the 3D large-$N_f$ continuous transitions between the disordered and the Higgs phase, where the flavor symmetry breaks to $\mathrm{SU}(2)\otimes \mathrm{U}(N_f-2)$. Therefore, at least for large enough $N_f$, the 3D SU($N_c$) gauge Higgs field theories with multicomponent scalar fields can be nonperturbatively defined by the continuum limit of lattice discretizatized models with the same local and global symmetries.