An effective action for finite temperature QCD with fermions

Using lattice perturbation theory at finite temperature, we compute for staggered fermions the one-loop fermionic corrections to the spatial and temporal plaquette couplings as well as the leading Z_N symmetry breaking coupling. Numerical and analytical considerations indicate that the finite temperature corrections to the zero-temperature calculation of A. Hasenfratz and T. DeGrand are small for small values of k = frac(1, 2 m_F), but become significant for intermediate values of κ. The effect of these finite temperature corrections is to ruin the agreement of the Hasenfratz-DeGrand calculation with Monte Carlo data. We conjecture that the finite temperature corrections axe suppressed nouperturbatively at low temperatures, resolving this apparent disagreement. The Z_N symmetry breaking coupling is small; we argue that it may change the order of the transition while having little effect on the critical value of β.