Matrix model for deconfinement in a SU(Nc) gauge theory in 2+1 dimensions

Abstract: We use an effective matrix model to study deconfinement in a pure SU(Nc) gauge theory, without quarks, in d=2+1 dimensions. Expanding about a constant background A0 field we construct an effective potential for the eigenvalues of the thermal Wilson line for general Nc and in the large-Nc limit. The numerical results are presented using one, two, and four free parameters, which are determined by fitting directly to the lattice data for the pressure. The matrix model shows a good agreement with numerical lattice simulations for the pressure and the interaction measure, starting from the perturbative limit up to the critical temperature. For the pressure, the details of A0- dependent nonperturbative terms are relevant only in a narrow transition region below ~1.2 Td. This is also the range where the Polyakov loop deviates notably from one. In accordance with the lattice results we find that, up to a trivial factor Nc^2-1, there is only a mild dependence on the number of colors.