Universal low-temperature behavior of two-dimensional lattice scalar chromodynamics

Abstract

We study the role that global and local nonabelian symmetries play in two-dimensional lattice gauge theories with multicomponent scalar fields. We start from a maximally O($M$)-symmetric multicomponent scalar model, Its symmetry is partially gauged to obtain an SU($N_c$) gauge theory (scalar chromodynamics) with global U$(N_f)$ (for $N_c\ge 3$) or Sp($N_f$) symmetry (for $N_c=2$), where $N_f>1$ is the number of flavors. Correspondingly, the fields belong to the coset $S^M$/SU($N_c$) where $S^M$ is the $M$-dimensional sphere and $M=2N_f{N}_c$. In agreement with the Mermin-Wagner theorem, the system is always disordered at finite temperature and a critical behavior only develops in the zero-temperature limit. Its universal features are investigated by numerical finite-size scaling methods. The results show that the asymptotic low-temperature behavior belongs to the universality class of the 2D CP${}^{N_f-1}$ field theory for $N_c>2$, and to that of the 2D Sp($N_f$) field theory for $N_c=2$. These universality classes correspond to 2D statistical field theories associated with symmetric spaces that are invariant under Sp($N_f$) transformations for $N_c=2$ and under SU($N_f$) for $N_c>2$. These symmetry groups are the same invariance groups of scalar chromodynamics, apart from a U(1) flavor symmetry that is present for $N_f\ge N_c>2$, which does not play any role in determining the asymptotic behavior of the model.

12 pages, 12 eps figures

References in corpus (5)

• Multicomponent compact Abelian-Higgs lattice models
• Phase diagram, symmetry breaking, and critical behavior of three-dimensional lattice multiflavor scalar chromodynamics
• Three-dimensional lattice multiflavor scalar chromodynamics: interplay between global and gauge symmetries
• Landau-Ginzburg Theories of Non-Abelian Quantum Hall States from Non-Abelian Bosonization
• Two-dimensional multicomponent Abelian-Higgs lattice models

Cited by in corpus (10)

• Coherent and dissipative dynamics at quantum phase transitions
• Critical behaviors of lattice U(1) gauge models and three-dimensional Abelian-Higgs gauge field theory
• Three-dimensional phase transitions in multiflavor lattice scalar SO(Nc) gauge theories
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Asymptotic low-temperature behavior of two-dimensional RP${}^{N-1}$ models
• Asymptotic low-temperature critical behavior of two-dimensional multiflavor lattice SO(Nc) gauge theories
• Two-dimensional lattice SU($N_c$) gauge theories with multiflavor adjoint scalar fields
• Berezinskii-Kosterlitz-Thouless transitions in two-dimensional lattice SO($N_c$) gauge theories with two scalar flavors
• Chiral critical behavior of 3D lattice fermionic models with quartic interactions
• Color-flavor reflection in the continuum limit of two-dimensional lattice gauge theories with scalar fields