The high temperature phase transition in SU(N) gauge theories

We calculate the continuum value of the deconfining temperature in units ofthe string tension for SU(4), SU(6) and SU(8) gauge theories, and werecalculate its value for SU(2) and SU(3). We find that the $N$-dependence for$2 \leq N \leq 8$ is well fitted by $T_c/\sqrt{sigma} = 0.596(4) +0.453(30)/N^2$, showing a rapid convergence to the large-N limit. We confirmour earlier result that the phase transition is first order for $N \geq 3$ andthat it becomes stronger with increasing $N$. We also confirm that as $N$increases the finite volume corrections become rapidly smaller and the phasetransition becomes visible on ever smaller volumes. We interpret the latter asbeing due to the fact that the tension of the domain wall that separates theconfining and deconfining phases increases rapidly with $N$. We speculate onthe connection to Eguchi-Kawai reduction and to the idea of a Master Field.Comment: 27 page