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

We consider three-dimensional (3D) lattice SU(Nc) gauge Higgs theories with multicomponent (Nf>1) degenerate scalar fields and U(Nf) global symmetry, focusing on systems with Nc=2, to identify critical behaviors that can be effectively described by the corresponding 3D SU(Nc) 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 Nf, that would control transitions characterized by the global symmetry-breaking pattern U(Nf)→SU(2) - U(Nf-2). Continuous transitions with the same symmetry-breaking pattern are observed in the SU(2) lattice gauge model for Nf≥30. Here we present a detailed finite-size scaling analysis of the Monte Carlo data for several large values of Nf. The results are in substantial agreement with the field-theoretical predictions obtained in the large-Nf limit. This provides evidence that the SU(Nc) gauge Higgs field theories provide the correct effective description of the 3D large-Nf continuous transitions between the disordered and the Higgs phase, where the flavor symmetry breaks to SU(2) - U(Nf-2). Therefore, at least for large enough Nf, the 3D SU(Nc) gauge Higgs field theories with multicomponent scalar fields can be nonperturbatively defined by the continuum limit of lattice discretized models with the same local and global symmetries.