Abstract
We put forward an alternative way to estimate the deconfinement temperature in bottom-up holographic models. The deconfinement in AdS/QCD is related to the Hawking-Page phase transition, in which the critical Hawking temperature is identified with the deconfinement one in the gauge theory. The numeric estimation of the latter is only possible when the parameters of a $5D$ dual model are previously determined from consistency with other physical aspects, standardly, providing a description of the QCD resonances. The traditional way to fix parameters in the simplest AdS/QCD models is to reproduce the mass of the $\rho$ meson or the slope of the approximate radial Regge trajectory of the $\rho$ excitations. Motivated by a general idea that the slope value originates in gluodynamics, we propose calculating the deconfinement temperature using the trajectory of scalar glueballs. We consider several holographic models and use the recent idea of isospectral potentials to make an additional check of the relevance of our approach. It is demonstrated that different models from an isospectral family (i.e. the models leading to identical predictions for spectrum of hadrons with fixed quantum numbers) result in different predictions for the deconfinement temperature. This difference is found to be quite small in the scalar glueball channel but very large in the vector meson channel. The observed stability in the former case clearly favours the choice of the glueball channel for thermodynamic predictions in AdS/QCD models. For a balanced approach, we argue that either assuming $f_0(1500)$ to have a dominating component of $0^{++}$ glueball or accepting the idea of the universality in the radial Regge trajectories of light non-strange vector mesons one can reproduce the results for the deconfinement temperature obtained before in the lattice simulations in the background of non-dynamical quarks.
Highlights
The anti-de Sitter (AdS)/QCD correspondence proved to be a useful technique to study different facets of the strongly coupled theories
Besides the established QCD content of mesons and baryons, one may try to apply the holography to the hypothesized QCD bound states—the glueballs
In Ref. [16], we showed that this value of μ2 leads to a consistent numerical estimation of the deconfinement temperature in the soft wall (SW) model
Summary
The anti-de Sitter (AdS)/QCD correspondence proved to be a useful technique to study different facets of the strongly coupled theories. (the interpolating operator G2μν is assumed [11]), and consider the scalar resonance f0ð1500Þ [3] as the lightest glueball (as is often proposed in the hadron spectroscopy [3]), we will obtain the slope μ2 1⁄4 1.13 GeV2 It agrees perfectly with the mean radial slope μ2 1⁄4 1.14 Æ 0.01 GeV2 found for the light mesons in the analysis [21] and achieved independently in Refs. We will demonstrate that such isospectral models, result in different predictions for the deconfinement temperature Tc. In the vector channel originally considered by Herzog in Ref. The original Herzog analysis of the vector hard wall (HW) holographic model with the ρ-meson taken as the lowest state resulted in the prediction Tc 1⁄4 122 MeV [15] If we apply this analysis to the scalar HW model with f0ð1500Þ as the lightest glueball, we will find Tc ≈ 150 MeV. VII with a discussion on the general validity of the presented approach
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