Thermodynamics of the QCD plasma and the large-N limit

TL;DR

The paper investigates equilibrium thermodynamics of SU($N$) Yang–Mills theories at finite temperature in the large-$N$ limit using lattice simulations for $N=3,4,5,6,8$ across $0.8T_c$ to $3.4T_c$, and extrapolates to $N\to\infty$. It finds that thermodynamic observables per gluon, such as pressure, energy density, entropy density, and the trace anomaly, show only mild dependence on $N$, supporting the applicability of large-$N$ models to the QCD plasma. The results are compared with the improved holographic QCD model and AdS/CFT-inspired predictions, showing good agreement in the deconfined regime and near quasi-conformal temperatures. A careful extrapolation to $N\to\infty$ yields a consistent large-$N description of the YM thermodynamics, reinforcing the relevance of holographic methods for QCD-like plasmas and providing a benchmark for future non-perturbative and holographic studies.

Abstract

The equilibrium thermodynamic properties of the SU(N) plasma at finite temperature are studied non-perturbatively in the large-N limit, via lattice simulations. We present high-precision numerical results for the pressure, trace of the energy-momentum tensor, energy density and entropy density of SU(N) Yang-Mills theories with N=3, 4, 5, 6 and 8 colors, in a temperature range from 0.8T_c to 3.4T_c (where T_c denotes the critical deconfinement temperature). The results, normalized according to the number of gluons, show a very mild dependence on N, supporting the idea that the dynamics of the strongly-interacting QCD plasma could admit a description based on large-N models. We compare our numerical data with general expectations about the thermal behavior of the deconfined gluon plasma and with various theoretical descriptions, including, in particular, the improved holographic QCD model recently proposed by Kiritsis and collaborators. We also comment on the relevance of an AdS/CFT description for the QCD plasma in a phenomenologically interesting temperature range where the system, while still strongly-coupled, approaches a `quasi-conformal' regime characterized by approximate scale invariance. Finally, we perform an extrapolation of our results to the N to $\infty$ limit.

Figures (10)

• Figure 1: (Color online) The dimensionless ratio $p/T^4$, normalized to the lattice SB limit $\pi^2(N^2-1)R_I(N_t)/45$, versus$T/T_c$, as obtained from simulations of $\mathrm{SU}(N)$ lattice gauge theories on $N_t=5$ lattices. Errorbars denote statistical uncertainties only. The results corresponding to different gauge groups are denoted by different colors, according to the legend. The yellow solid line denotes the prediction from the improved holographic QCD model from ref. Gursoy:2009jd (with a trivial, parameter-free rescaling to our normalization).
• Figure 2: (Color online) Same as in fig. \ref{['fig:pressure']}, but for the $\Delta/T^4$ ratio, normalized to the SB limit of $p/T^4$.
• Figure 3: (Color online) Same as in fig. \ref{['fig:pressure']}, but for the $\epsilon/T^4$ ratio, normalized to the SB limit.
• Figure 4: (Color online) Same as in fig. \ref{['fig:pressure']}, but for the $s/T^3$ ratio, normalized to the SB limit.
• Figure 5: (Color online) The $\mathrm{SU}(N)$ lattice equation of state, expressed as $p(\epsilon)$, and the approach to conformality (dotted line). The dashed curve denotes the prediction from the $\mathrm{SU}(3)$ weak-coupling expansion Hietanen:2008tv.