We address the interplay between local and global symmetries by analyzing the continuum limit of two-dimensional multicomponent scalar lattice gauge theories, endowed by non-Abelian local and global invariance. These theories are asymptotically free. By exploiting Monte Carlo simulations and finite-size
scaling techniques, we provide numerical results concerning the universal
behavior of such models in the critical regime. Our results support the
conjecture that two-dimensional multiflavor scalar models have the same
continuum limit as the $\sigma$-models
associated with symmetric spaces that have the same global symmetry.