Properties of the deconfining phase transition in SU(N) gauge theories -: art. no. 033

We extend our earlier investigation of the finite temperature deconfinement transition in SU(N) gauge theories, with the emphasis on what happens as N --> infinity. We calculate the latent heat, L-h, in the continuum limit, and find the expected behaviour, L-h proportional to N-2, at large N. We confirm that the phase transition, which is second order for SU(2) and weakly first order for SU(3), becomes robustly first order for N >= 4 and strengthens as N increases. As an aside, we explain why the SU(2) specific heat shows no sign of any peak as T is varied across what is supposedly a second order phase transition. We calculate the effective string tension and electric gluon masses at T similar or equal to T-c confirming the discontinuous nature of the transition for N >= 3. We explicitly show that the large-N 'spatial' string tension does not vary with T for T <= T-c and that it is discontinuous at T - T-c. For T >= T-c it increases proportional to T-2 to a good approximation, and the k-string tension ratios closely satisfy Casimir Scaling. Within very small errors, we find a single T-c at which all the k-strings deconfine, i.e. a step-by-step breaking of the relevant centre symmetry does not occur. We calculate the interface tension but are unable to distinguish between the proportional to N or proportional to N-2 variations, each of which can lead to a striking but different N = infinity deconfinement scenario. We remark on the location of the bulk phase transition, which bounds the range of our large-N calculations on the strong coupling side, and within whose hysteresis some of our larger-N calculations are performed.