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

Abstract

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 ∝ 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 ≃ 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 ∝ 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 ∝ 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.

Introductory lectures to large- QCD phenomenology and lattice results

“…For larger values of N, the deconfinement transition becomes a discontinuous (i.e. first order) one: this is seen in the SU(3) theory [173] and-even more clearly-for all SU(N) theories with N ≥ 4 [155,156,162]. Intuitively, the change to a (more and more strongly) first-order transition as the number of color charges is increased can be interpreted in terms of a more and more "violent" transition, which takes place at the temperature where the free energies of a gas of glueballs (whose number is O(N 0 )) and of gluons (with O(N 2 ) degrees of freedom) become equal.…”

“…The first-order nature of the deconfinement transition for N ≥ 3 is associated to the finiteness of the latent heat L h , which scales like O(N 2 ) in the large-N limit [156,161]:…”

“…Similarly, a first-order deconfinement transition also implies a non-vanishing value for the surface tension associated with interfaces between the confining and deconfined phases [156] …”

Closed flux tubes and their string description in D=2+1 SU(N) gauge theories

“…Another difference is that in D = 2 + 1 the deconfining transition is second order for SU (2) and SU(3), weakly first order for SU (4), and only becomes robustly first order for N ≥ 5 [10][11][12][13], whereas in D = 3 + 1 it is already first order for SU(3) [17][18][19]. Since the behaviour of flux tubes of length l will be governed by the critical exponents of the second order transition as l approaches l c = 1/T c , and these are given by the universality class of a spin model in one lower dimension, we need to consider at least N ≥ 4 or possibly N ≥ 5 if we wish to investigate the large-N stringy behaviour of flux tubes down to values of l that are close to l c .…”

Lattice baryons in the1/Nexpansion

“…There is also a literature of lattice simulations applied to gauge theories with the group SU(N), for moderately large N. Most of it [3][4][5][6][7][8][9][10] is directed at the properties of pure gauge theory. I know of two papers on meson spectroscopy: Refs.…”