Charged critical behavior and nonperturbative continuum limit of three-dimensional latticeSU⁡(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.