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

Abstract

We calculate the continuum value of the deconfining temperature in units of the string tension for SU(4), SU(6) and SU(8) gauge theories, and we recalculate its value for SU(2) and SU(3). We find that the N-dependence for 2 ≤ N ≤ 8 is well fitted by T c / √ σ = 0.596(4) + 0.453(30)/N 2 , showing a rapid convergence to the large-N limit. We confirm our earlier result that the phase transition is first order for N ≥ 3 and that it becomes stronger with increasing N. We also confirm that as N increases the finite volume corrections become rapidly smaller and the phase transition becomes visible on ever smaller volumes. We interpret the latter as being due to the fact that the tension of the domain wall that separates the confining and deconfining phases increases rapidly with N. We speculate on the connection to Eguchi-Kawai reduction and to the idea of a Master Field.

Thermal dilepton rate and electrical conductivity: An analysis of vector current correlation functions in quenched lattice QCD

“…It is known to give the variation of the lattice cut-off as function of the gauge coupling to better than 1% in the interval [5.6, 6.5] [30]. We added to this analysis new results for the critical coupling β c (N τ ) and the square root of the string tension √ σ [31] and extrapolated the fit results to the regime of couplings relevant for our analysis, i.e. β ∈ [6.8, 7.8].…”

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 .…”

“…that the critical deconfining length scale is larger, l c √ σ ∼ 1.5, in D = 3 + 1 [17][18][19] than it is in D = 2 + 1 [10][11][12][13], where l c √ σ ∼ 1. So in D = 2 + 1 we can access significantly shorter flux tubes than in D = 3 + 1.…”

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.…”