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

• Published in: arXiv.org 2024-09
• Main Authors: Bonati, Claudio, Pelissetto, Andrea, Ivan Soler Calero, Vicari, Ettore
• Format: Article
• Language: English
• Subjects: Broken symmetry; Field theory; Flavor (particle physics); Scalars; Symmetry
• ISSN: 2331-8422

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.