Properties of the deconfining phase transition in SU(N) gauge theories - Lucini, B; Teper, M; Wenger, U (2005)
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, Lh, in the continuum limit, and find the expected behaviour, Lh ∝ 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 ≃ Tc 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 ≤ Tc and that it is discontinuous at T = Tc. For T ≥ Tc 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 ∝ N 2 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. © SISSA/ISAS 2005.