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

• Published in: Physical review. D 2024-11, Vol.110 (9), Article 094504
• Main Authors: Bonati, Claudio, Pelissetto, Andrea, Soler Calero, Ivan, Vicari, Ettore
• Format: Article
• Language: English
• ISSN: 2470-0010; 2470-0029
• DOI: 10.1103/PhysRevD.110.094504

We consider 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 U ( N f ) → SU ( 2 ) ⊗ U ( N f − 2 ) . Continuous transitions with the same symmetry-breaking pattern are observed in the SU(2) lattice gauge model for N f ≥ 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 SU ( 2 ) ⊗ 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 discretized models with the same local and global symmetries.