Three-dimensional lattice multiflavor scalar chromodynamics: Interplay between global and gauge symmetries

We study the nature of the finite-temperature transition of the three-dimensional scalar chromodynamics with N-f flavors. These models are constructed by considering maximally O(M)-symmetric multicomponent scalar models, whose symmetry is partially gauged to obtain SU(N-c) gauge theories, with a residual nonabelian global symmetry given by U(N-f) for N-c >= 3 and Sp(N-f) for N-c = 2, so that M = 2N(c)N(f). For N-f = 2 and for all values of N-c we investigated, N-c = 2, 3, 4, these systems undergo a continuous finite-temperature transition, which belongs to a universality class related to the global symmetry group of the model. For N-c = 2, since Sp(2)/Z(2) = SO(5), it belongs to the O(5) vector universality class. For N-c >= 3, since SU(2)/Z(2) = SO(3), it belongs to the O(3) vector universality class. For N-f >= 3, the numerical results show evidence of first-order transitions for any N-c. These results are in agreement with the predictions obtained by using the effective Landau-Ginzburg-Wilson approach in terms of a gauge-invariant order parameter. Our results indicate that the non-Abelian gauge degrees of freedom are irrelevant at the transition. These conclusions are supported by an analysis of gauge-field dependent correlation functions, that are always short ranged, even at the transition.