Thermodynamics of the QCD plasma and the large-N limit (0907.3719v2)

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.

• The paper presents high-precision lattice results for pressure, energy density, and entropy to map the thermal behavior of SU(N) plasmas.
• The paper shows that normalized thermodynamic observables display only mild N dependence, supporting large-N extrapolation methods.
• The paper validates improved holographic QCD models by comparing lattice data with theoretical predictions, reinforcing their role in describing sQGP dynamics.

Thermodynamics of the QCD Plasma and the Large-$N$ Limit

The thermodynamic behavior of quantum chromodynamics (QCD) plasmas, especially at high temperatures beyond the critical deconfinement temperature $T_c$, has drawn considerable interest due to its implications for understanding strongly-coupled systems like the quark-gluon plasma (QGP). In this paper by Marco Panero, the thermodynamics of the $SU(N)$ plasma for large $N$ is investigated using lattice simulations, focusing on Yang-Mills theories with $N = 3, 4, 5, 6$, and $8$ colors. This paper explores the possibility of employing large-$N$ models to describe the dynamics of such systems, supported by the results that indicate minimal dependence on $N$.

Key Results

1. Thermodynamic Observables: The paper provides high-precision lattice results for pressure, trace of the energy-momentum tensor, energy density, and entropy density across a range of temperatures from $0.8T_c$ to $3.4T_c$. These quantities were found to show a mild $N$ dependence when normalized to the number of gluons.
2. Large-$N$ Dynamics: An extrapolation to the $N \to \infty$ limit was performed, which provides insight into the emergent behavior in this limit. The findings support the applicability of large-$N$ techniques to describe QCD plasmas, consistent with the assumption of the large-$N$ equivalence in QCD behavior.
3. Comparison with Theoretical Models: Lattice results were compared with theoretical expectations and models, including holographic QCD approaches, which leverage analogies with gravity. Notably, the improved holographic QCD model fits the data owing to its ability to capture features like nearly conformal behavior at high temperatures.

Theoretical Implications

• Holographic Models and AdS/CFT: The results underscore the relevance of holographic models, particularly in regimes where QCD becomes nearly conformal, aiding in the understanding of sQGP dynamics. The improved holographic QCD model by Kiritsis et al. aligns well with lattice results, fortifying the theoretical connection established by the AdS/CFT correspondence in large-$N$ limits.
• Perturbation Theory: Traditional perturbative expansions at finite temperature QCD show limitations, particularly close to $T_c$. The paper suggests additional non-perturbative contributions, aligning with a "fuzzy bag" model that incorporates temperature-dependent terms overlooked in naive perturbative studies.

Practical and Theoretical Impact

Extrapolating results to the large-$N$ limit provides groundwork for future theoretical advancements in understanding not just QCD, but potentially any strongly-coupled gauge theory. Practically, the insights from such models have implications for experiments in heavy-ion collisions where QGP is studied.

Future Directions

Continuing from these findings, potential research could explore the equilibrium and non-equilibrium properties of QCD and its analogs across different dimensions and gauge groups. Expanding such studies might include more complex fermionic interactions or exploring modified lattice actions that hone in more subtly on infra-red phenomena within the plasma.

In conclusion, this thorough lattice-based investigation of $SU(N)$ Yang-Mills theory within the context of QCD plasma thermodynamics provides a compelling quantitative base supporting large-$N$ limits. It offers both directions for new theoretical developments and validation of certain non-perturbative models in describing components of the strong force.