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

Abstract

We use matrix models to characterize deconfinement at a nonzero temperature T for an SU(2) gauge theory in three spacetime dimensions. At one loop order, the potential for a constant vector potential A0 is ~T^3 times a trilogarithm function of A0/T. In addition, we add various nonperturbative terms to model deconfinement. The parameters of the model are adjusted by fitting the lattice results for the pressure. The nonperturbative terms are dominated by a constant term ~T^2Td, where Td is the temperature for deconfinement. Besides this constant, we add terms which are nontrivial functions of A0/T, both ~T^2Td and ~TTd^2. There is only a mild sensitivity to the details of these nonconstant terms. Overall we find a good agreement with the lattice results. For the pressure, the conformal anomaly, and the Polyakov loop the nonconstant terms are relevant only in a narrow region below ~1.2Td. We also compute the 't Hooft loop, and find that the details of the nonconstant terms enter in a much wider region, up to ~4Td.