Thermodynamics of the QCD Plasma and the Large-NLimit

Abstract

The equilibrium thermodynamic properties of the SU(N) plasma are studied nonperturbatively in the large-N limit, via high-precision lattice simulations at temperatures from 0.8T(c) to 3.4T(c) (T(c) being the critical deconfinement temperature). Our results for SU(N) Yang-Mills theories with N=3, 4, 5, 6, and 8 colors show a very mild dependence on N, supporting the idea that the QCD plasma could be described by models based on the large-N limit. We compare our data with various theoretical descriptions, including, in particular, the improved holographic QCD model proposed by Kiritsis and collaborators. We also comment on the relevance of an AdS/CFT description in a phenomenologically interesting temperature range where the system, while still strongly coupled, becomes approximately scale invariant. Finally, we extrapolate our results to the N --> infinity limit.

Introductory lectures to large- QCD phenomenology and lattice results

“…There exist also a number of works investigating the finite-temperature properties via Monte Carlo simulations [155][156][157][158][159][160][161][162][163][164][165][166]. These works give convincing evidence that all SU(N) Yang-Mills theories undergo a physical deconfining transition at a critical temperature T c , which remains finite when expressed in some appropriately defined non-perturbative scale of the theory (e.g.…”

“…Another finding discussed in refs. [161,163] is that, as shown in fig. 19, at temperatures of the same order of magnitude of T c , the trace anomaly ∆ in the deconfined phase seems to be approximately proportional to T 2 : a Figure 18: The renormalized fundamental Polyakov loop computed in ref.…”

“…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]:…”

“…The dependence of the free energy of non-Abelian gauge theories on the temperature (or the "equation of state") has been studied via lattice simulations in refs. [158,[160][161][162][163]: in the deconfined phase at T > T c , all equilibrium thermodynamic quantities (such as the pressure p, the trace anomaly ∆, and the energy and entropy densities ǫ and s) are exactly proportional to the number of gluon degrees of freedom, 2(N 2 − 1), with essentially the same dependence on T /T c in all SU(N ≥ 3) theories. In fact, the dependence of the equation of state on the number of colors (up to the trivial gluon multiplicity factor) appears to be even milder than for other quantities, so that the equilibrium thermodynamics properties of the "physical" theory with N = 3 colors are basically the same as those of the large-N theory.…”

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.…”