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

Caselle, Michele; Nada, Alessandro; Panero, Marco

doi:10.1007/jhep07(2015)143

Cited by 44 publications

(56 citation statements)

References 139 publications

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“…[21], and extends it with configurations on finer lattices, enabling us to extrapolate our results to the continuum limit.…”

Section: A Results For the Su(2) Theorymentioning

confidence: 73%

“…As shown in various recent works [18][19][20][21], the contribution from a tower of Hagedorn states to pure Yang-Mills thermodynamics is non-negligible. In the present analysis, we consider the same Hagedorn spectrum used in Ref.…”

Section: A Results For the Su(2) Theorymentioning

confidence: 89%

“…The success of this "ideal" hadron-resonance-gas model in describing the QCD thermodynamics in the confining phase is also confirmed by its comparison with numerical results from lattice calculations, which are based on the first principles of the theory, without any model-dependent assumptions. This has been shown for full QCD with dynamical fermions [16,17], as well as for pure Yang-Mills theory 1 [18][19][20][21], and even in 2 þ 1 spacetime dimensions [22]. While the behavior of bulk thermodynamic quantities at very low temperatures is essentially accounted for by the contributions of the lightest hadron species only, heavier states start to play a more prominent role at temperatures Oð10 2 Þ MeV: in particular, in Hagedorn's original picture [10], which predates QCD, an exponential growth in the hadron spectral density as a function of mass implies the existence of a limiting, maximal temperature at which hadronic matter can exist.…”

Section: Introductionmentioning

confidence: 75%

“…This data sample includes part of the data used in Ref. [21]. N t N sÑ n β β range n conf at finite T n conf at T ¼ 0 …”

Section: A Results For the Su(2) Theorymentioning

confidence: 99%

“…[21]; we refer readers interested in technical details about the lattice calculation to that article, and to the earlier works mentioned therein.…”

Section: Lattice Setupmentioning

confidence: 99%

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Excluded-volume effects for a hadron gas in Yang-Mills theory

et al. 2017

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When the multiplicities of particles produced in heavy-ion collisions are fitted to the hadron-resonancegas model, excluded-volume effects play a significant role. In this work, we study the impact of such effects on the equation of state of pure Yang-Mills theory at low temperatures, comparing the predictions of the statistical model with lattice results. In particular, we present a detailed analysis of the SU(2) and SU(3) Yang-Mills theories: we find that, for both of them, the best fits to the equilibrium thermodynamic quantities are obtained when one assumes that the volume of different glueball states is inversely proportional to their mass. The implications of these findings for QCD are discussed.

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“…[21], and extends it with configurations on finer lattices, enabling us to extrapolate our results to the continuum limit.…”

Section: A Results For the Su(2) Theorymentioning

confidence: 73%

Section: A Results For the Su(2) Theorymentioning

confidence: 89%

Section: Introductionmentioning

confidence: 75%

“…This data sample includes part of the data used in Ref. [21]. N t N sÑ n β β range n conf at finite T n conf at T ¼ 0 …”

Section: A Results For the Su(2) Theorymentioning

confidence: 99%

“…[21]; we refer readers interested in technical details about the lattice calculation to that article, and to the earlier works mentioned therein.…”

Section: Lattice Setupmentioning

confidence: 99%

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Excluded-volume effects for a hadron gas in Yang-Mills theory

et al. 2017

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On the Hagedorn temperature in holographic confining gauge theories

Bigazzi

Canneti

Cotrone

2023

J. High Energ. Phys.

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The divergence of the string partition function due to the exponential growth of states is a well-understood issue in flat spacetime. It can be interpreted as the appearance of tachyon modes above a certain temperature, known as the Hagedorn temperature TH. In the literature, one can find some intuitions about its generalization to curved spacetimes, where computations are extremely hard and explicit results cannot be provided in general. In this paper, we present a genus-zero estimate of TH, at leading order in α′, for string theories on curved backgrounds holographically dual to confining gauge theories. This is a particularly interesting case, since the holographic correspondence equates TH with the Hagedorn temperature of the dual gauge theories. For concreteness we focus on Type IIA string theory on a well known background dual to an SU(N) Yang-Mills theory. The resulting Hagedorn temperature turns out to be proportional to the square root of the Yang-Mills confining string tension. The related coefficient, which at leading order is analytically determined, is the same as the one for Type II theories in flat space. While the calculation is performed in a specific model, the result applies in full generality to confining gauge theories with a top-down holographic dual.

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Conformal field theory and the hot phase of three-dimensional U(1) gauge theory

Caselle

Nada

Panero

et al. 2019

J. High Energ. Phys.

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We study the high-temperature phase of compact U(1) gauge theory in 2 + 1 dimensions, comparing the results of lattice calculations with analytical predictions from the conformalfield-theory description of the low-temperature phase of the bidimensional XY model. We focus on the two-point correlation functions of probe charges and the field-strength operator, finding excellent quantitative agreement with the functional form and the continuously varying critical indices predicted by conformal field theory. arXiv:1903.00491v2 [cond-mat.str-el] 13 May 2019Polyakov loop can be directly related to the free energy associated with a chromoelectric probe charge: in the thermodynamic limit P vanishes for T < T c (implying an infinite energy cost for the existence of an isolated fundamental color source in the confining phase, i.e. quark confinement), whereas it has a finite expectation value at T > T c . In contrast, the U(1) center symmetry of U(1) gauge theory in 2 + 1 dimensions remains unbroken, and, while in the high-temperature phase the theory does not have a dynamically generated, finite, characteristic length scale, the logarithmic Coulomb potential is still sufficient to confine static charges.As the finite-temperature transition in U(1) gauge theory in 2 + 1 dimensions is continuous, one expects that at T = T c the long-distance properties of the system are equivalent to those of a two-dimensional spin system with global U(1) symmetry [116], i.e. the classical XY model, that exhibits a Kosterlitz-Thouless transition [117] (see also refs. [118-121]). In the past, the validity of this conjecture has been investigated in various numerical studies [87,[101][102][103] and the most recent work gives conclusive evidence in support of it [104].As discussed in ref. [116], this correspondence relies on the continuous nature of the transition at T = T c . In turn, the existence of an infinite correlation length is also an essential necessary condition for scale and conformal invariance. In the two-dimensional XY model, this condition is realized in a peculiar way: even though the system can never have spontaneous magnetization [122], at low temperatures the model is in a phase characterized by "topological" order [117], with two-point spin correlation functions decaying only with inverse powers of the spatial separation r between the spins [123,124]. The fact that the whole low-temperature phase of the two-dimensional XY model is gapless and admits a conformal-field-theory description raises the question, what happens in the corresponding phase of the three-dimensional gauge theory, i.e. the high-temperature phase? To answer this question, in this work we carry out a systematic study of compact U(1) lattice gauge theory at T > T c , and compare a large set of novel numerical results, obtained by Monte Carlo simulations, with analytical predictions derived from conformal field theory. Specifically, we focus our attention on correlation functions of plaquette operators, Polyakov loops, and on the profile of the flux tube ind...

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

Cited by 44 publications

References 139 publications

Excluded-volume effects for a hadron gas in Yang-Mills theory

Excluded-volume effects for a hadron gas in Yang-Mills theory

On the Hagedorn temperature in holographic confining gauge theories

Conformal field theory and the hot phase of three-dimensional U(1) gauge theory

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