Hagedorn spectrum and thermodynamics of SU(2) and SU(3) Yang-Mills theories

Abstract

We present a high-precision lattice calculation of the equation of state in the confining phase of SU(2) Yang-Mills theory. We show that the results are described very well by a gas of massive, non-interacting glueballs, provided one assumes an exponentially growing Hagedorn spectrum. The latter can be derived within an effective bosonic closed-string model, leading to a parameter-free theoretical prediction, which is in perfect agreement with our lattice results. Furthermore, when applied to SU(3) Yang-Mills theory, this effective model accurately describes the lattice results reported by Borsányi et al. in JHEP 07 (2012) 056.

1+19 pages, 4 pdf figures; v2: 1+22 pages, 4 pdf figures, improved discussion in sections 3 and 4, added references, corrected misprints: matches the journal version; v3: corrected a misprint, pointed out to us by Etsuko Itou, in the discussion of eq. (3.1), results unaffected

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Cited by in corpus (28)

• Non-Abelian Dark Forces and the Relic Densities of Dark Glueballs
• Effective string description of confining flux tubes
• QCD thermodynamics from lattice calculations with non-equilibrium methods: The SU(3) equation of state
• Matching the Hagedorn mass spectrum with Lattice QCD results
• Jarzynski's theorem for lattice 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
• Exploring the Universe with Dark Light Scalars
• Excluded-volume effects for a hadron gas in Yang-Mills theory
• Nonperturbative SU(3) thermodynamics and the phase transition
• Confinement-Deconfinement Crossover in the Lattice $\mathbb{C}{P}^{N-1}$ Model
• Improved thermodynamics of SU(2) gauge theory
• Themodynamics for pure SU($2$) gauge theory using gradient flow
• Strong coupling from non-equilibrium Monte Carlo simulations
• Scaling behavior of regularized bosonic strings
• Duality transformations and the entanglement entropy of gauge theories
• Thermodynamics of the Glueball Resonance Gas
• Charting the scaling region of the Ising universality class in two and three dimensions
• On the $T\bar{T}$ deformation of the compactified boson and its interpretation in Lattice Gauge Theory
• On the Hagedorn Temperature in Holographic Confining Gauge Theories
• Conformal field theory and the hot phase of three-dimensional U(1) gauge theory
• Hagedorn temperature in holography: world-sheet and effective approaches
• Conformal perturbation theory confronts lattice results in the vicinity of a critical point
• Investigation of the ensemble of maximal center gauge
• Perturbative width of open rigid strings
• $\xi /{\xi }_{2nd}$ ratio as a tool to refine Effective Polyakov Loop models
• Nonlinear Regge trajectories and saturation of the Hagedorn spectrum
• Holographic Hagedorn Temperature: Strong Coupling, Flavor and $\theta$-angle Effects
• On the equation of state of U(1) lattice gauge theory in three dimensions