Scaling and the continuum limit of the finite temperature deconfinement transition in SU(Nc) pure gauge theory

We investigated the finite temperature (T) phase transition for SU(N-c) gauge theory with N-c=4, 6, 8 and 10 at lattice spacing, a, of 1/(6T) or less. We checked that these theories have first-order transitions at such small a. In many cases we were able to find the critical couplings with precision as good as a few parts in 10(4). We also investigated the use of two-loop renormalization group equations in extrapolating the lattice results to the continuum, thus fixing the temperature scale in units of the phase transition temperature, T-c. We found that when a < 1/(8T(c)) the two-loop extrapolation was accurate to about 1%-2%. However, we found that trading T-c for the QCD scale, Lambda(MS), increases uncertainties significantly, to the level of about 5%-10%.