Comments on Yang-Mills thermodynamics, the Hagedorn spectrum and the gluon gas

Abstract

We discuss the dependence of pure Yang-Mills equation of state on the choice of gauge algebra. In the confined phase, we generalize to an arbitrary simple gauge algebra Meyer's proposal of modelling the Yang-Mills matter by an ideal glueball gas in which the high-lying glueball spectrum is approximated by a Hagedorn spectrum of closed-bosonic-string type. Such a formalism is undefined above the Hagedorn temperature, corresponding to the phase transition toward a deconfined state of matter in which gluons are the relevant degrees of freedom. Under the assumption that the adjoint string tension and the typical energy scale of the running coupling are gauge-algebra independent, we discuss about how the behavior of thermodynamical quantities such as the trace anomaly should depend on the gauge algebra in both the confined and deconfined phase. The obtained results compare favourably with recent and accurate lattice data in the $\mathfrak{su}(3)$ case and support the idea that the more the gauge algebra has generators, the more the phase transition is of first-order type.

Discussion extended in v2 ; to appear in Phys Lett B

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• SU(N) gauge theories at large N
• Precision SU(3) lattice thermodynamics for a large temperature range
• Non-Abelian Dark Forces and the Relic Densities of Dark Glueballs
• Thermodynamics of SU(N) Yang-Mills theories in 2+1 dimensions II - The deconfined phase
• Hagedorn spectrum and thermodynamics of SU(2) and SU(3) Yang-Mills theories
• Jarzynski's theorem for lattice gauge theory
• Exceptional thermodynamics: The equation of state of G(2) gauge theory
• Glueballs amass at RHIC and LHC Colliders! - The early quarkless 1st order phase transition at $T=270$ MeV - from pure Yang-Mills glue plasma to GlueBall-Hagedorn states
• Excluded-volume effects for a hadron gas in Yang-Mills theory
• Glueballs and the Yang-Mills plasma in a $T$-matrix approach
• The SUSY Yang-Mills plasma in a $T$-matrix approach
• Universal aspects in the equation of state for Yang-Mills theories
• Hagedorn spectrum and equation of state of Yang-Mills theories