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

We study the role that global and local non-Abelian symmetries play in two-dimensional (2D) 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(Nc) gauge theory (scalar chromodynamics) with global U(Nf) (for Nc≥3) or Sp(Nf) symmetry (for Nc=2), where Nf>1 is the number of flavors. Correspondingly, the fields belong to the coset SM/SU(Nc) where SM is the M-dimensional sphere and M=2NfNc. 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 CPNf-1 field theory for Nc>2 and to that of the 2D Sp(Nf) field theory for Nc=2. These universality classes correspond to 2D statistical field theories associated with symmetric spaces that are invariant under Sp(Nf) transformations for Nc=2 and under SU(Nf) for Nc>2. These symmetry groups are the same invariance groups of scalar chromodynamics, apart from a U(1) flavor symmetry that is present for Nf≥Nc>2, which does not play any role in determining the asymptotic behavior of the model.