  We address the interplay between global and local gauge nonabelian symmetries
in lattice gauge theories with multicomponent scalar fields. We consider
two-dimensional lattice scalar nonabelian gauge theories with a local SO(Nc)
(Nc >= 3) and a global O(Nf) invariance, obtained by partially gauging a
maximally O(Nf x Nc)-symmetric multicomponent scalar model. Correspondingly,
the scalar fields belong to the coset S(Nf Nc-1)/SO(Nc), where S(N) 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 nonabelian 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) sigma 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 RP(Nf-1) model.
