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(N-c) gauge theory (scalar chromodynamics) with global U(N-f) (for N-c >= 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 SM/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 >= N-c > 2, which does not play any role in determining the asymptotic behavior of the model.