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 ZN 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 κ=1/(2mF) 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 are suppressed nonperturbatively at low temperatures, resolving this apparent disagreement. The ZN 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. ((orig.))