Scaling and the continuum limit of the finite temperature deconfinement transition in SU(N<SUB>c</SUB>) pure gauge theory

We investigated the finite temperature (T) phase transition for SU(Nc) gauge theory with Nc=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 104. 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, Tc. We found that when a≤1/(8Tc) the two-loop extrapolation was accurate to about 1%-2%. However, we found that trading Tc for the QCD scale, ∧MS- , increases uncertainties significantly, to the level of about 5%-10%