Asymptotic low-temperature critical behavior of two-dimensional multiflavor lattice so (Nc) gauge theories

We address the interplay between global and local gauge non-Abelian symmetries in lattice gauge theories with multicomponent scalar fields. We consider two-dimensional lattice scalar non-Abelian gauge theories with a local SO(Nc) (Nc≥3) and a global O(Nf) invariance, obtained by partially gauging a maximally O(NfNc)-symmetric multicomponent scalar model. Correspondingly, the scalar fields belong to the coset SNfNc-1/SO(Nc), where SN is the N-dimensional sphere. In agreement with the Mermin-Wagner theorem, these lattice SO(Nc) gauge models with Nf≥3 do not have finite-temperature transitions related to the breaking of the global non-Abelian O(Nf) symmetry. However, in the zero-temperature limit they show a critical behavior characterized by a correlation length that increases exponentially with the inverse temperature, similarly to nonlinear O(N) σ models. Their 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 two-dimensional RPNf-1 model