Properties of the deconfining phase transition in SU(N) gauge theories

We extend our earlier investigation of the finite temperature deconfinement transition in SU(N) gauge theories, with the emphasis on what happens as N→∞. We calculate the latent heat, L_h, in the continuum limit, and find the expected behaviour, L_h∝N², 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 ≃ 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 ∝T² 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 ∝N or ∝N² variations, each of which can lead to a striking but different N = ∞ 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.