Three-dimensional lattice multiflavor scalar chromodynamics: Interplay between global and gauge symmetries
Claudio Bonati, Andrea Pelissetto, Ettore Vicari
Abstract
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 $\mathrm{O}(M)$-symmetric multicomponent scalar models, whose symmetry is partially gauged to obtain $\mathrm{SU}({N}_{c})$ gauge theories, with a residual nonabelian global symmetry given by $U({N}_{f})$ for ${N}_{c}\ensuremath{\ge}3$ and $\mathrm{Sp}({N}_{f})$ for ${N}_{c}=2$, so that $M=2{N}_{c}{N}_{f}$. 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 $\mathrm{Sp}(2)/{\mathbb{Z}}_{2}=\mathrm{SO}(5)$, it belongs to the O(5) vector universality class. For ${N}_{c}\ensuremath{\ge}3$, since $\mathrm{SU}(2)/{\mathbb{Z}}_{2}=\mathrm{SO}(3)$, it belongs to the O(3) vector universality class. For ${N}_{f}\ensuremath{\ge}3$, 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.