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 Nf flavors. These models are constructed by considering maximally O(M)-symmetric multicomponent scalar models, whose symmetry is partially gauged to obtain SU(Nc) gauge theories, with a residual nonabelian global symmetry given by U(Nf) for Nc≥3 and Sp(Nf) for Nc=2, so that M=2NcNf. For Nf=2 and for all values of Nc we investigated, Nc=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 Nc=2, since Sp(2)/Z2=SO(5), it belongs to the O(5) vector universality class. For Nc≥3, since SU(2)/Z2=SO(3), it belongs to the O(3) vector universality class. For Nf≥3, the numerical results show evidence of first-order transitions for any Nc. 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.