Machine learning holographic black hole from lattice QCD equation of state

Machine learning holographic black hole from lattice QCD equation of state

April 2, 2024 | Xun Chen, Mei Huang
This paper presents a machine learning approach to construct an analytic holographic black hole metric in the Einstein-Maxwell-Dilaton (EMD) framework, based on lattice QCD results for the equation of state (EOS) and baryon number susceptibility at zero baryon chemical potential. The dilaton potentials derived from the EMD framework are in good agreement with extended non-conformal DeWolfe-Gubser-Rosen (DGR) type potentials fixed by lattice QCD EOS, demonstrating the robustness of the EMD framework. The predicted critical endpoint (CEP) in the 2+1-flavor system is located at (T^c = 0.094 GeV, μ_B^c = 0.74 GeV), which is close to results from the Polyakov-Nambu-Jona-Lasinio (PNJL) model, functional renormalization group (FRG), and extended DGR holographic models. The study uses machine learning to determine the bulk metric and other parameters from lattice QCD data. A deep neural network is trained to predict entropy and baryon number susceptibility from temperature data. The model successfully reproduces lattice results for entropy density, pressure, energy density, and trace anomaly for pure gluon, 2-flavor, and 2+1-flavor systems. The results for the dilaton field φ(z) and baryon number susceptibility χ_B^2 are in good agreement with lattice results for 2-flavor and 2+1-flavor systems at zero chemical potential. The CEP location for the 2-flavor system is (μ_B^c = 0.46 GeV, T^c = 0.147 GeV), and for the 2+1-flavor system is (μ_B^c = 0.74 GeV, T^c = 0.094 GeV). These results are consistent with other non-perturbative models such as DSE-FRG, FRG, and the extended DGR model. The predicted CEP for the 2+1-flavor system is close to recent results from these models. The study shows that the EMD framework with machine learning provides a robust description of QCD matter at finite temperature and chemical potential. The results suggest that dynamic quarks influence the location of the CEP. This work represents the first attempt to construct an analytical holographic model using machine learning, offering insights into the QCD phase diagram and hadron spectra. Future work aims to incorporate more information into the holographic QCD model to make it more realistic.This paper presents a machine learning approach to construct an analytic holographic black hole metric in the Einstein-Maxwell-Dilaton (EMD) framework, based on lattice QCD results for the equation of state (EOS) and baryon number susceptibility at zero baryon chemical potential. The dilaton potentials derived from the EMD framework are in good agreement with extended non-conformal DeWolfe-Gubser-Rosen (DGR) type potentials fixed by lattice QCD EOS, demonstrating the robustness of the EMD framework. The predicted critical endpoint (CEP) in the 2+1-flavor system is located at (T^c = 0.094 GeV, μ_B^c = 0.74 GeV), which is close to results from the Polyakov-Nambu-Jona-Lasinio (PNJL) model, functional renormalization group (FRG), and extended DGR holographic models. The study uses machine learning to determine the bulk metric and other parameters from lattice QCD data. A deep neural network is trained to predict entropy and baryon number susceptibility from temperature data. The model successfully reproduces lattice results for entropy density, pressure, energy density, and trace anomaly for pure gluon, 2-flavor, and 2+1-flavor systems. The results for the dilaton field φ(z) and baryon number susceptibility χ_B^2 are in good agreement with lattice results for 2-flavor and 2+1-flavor systems at zero chemical potential. The CEP location for the 2-flavor system is (μ_B^c = 0.46 GeV, T^c = 0.147 GeV), and for the 2+1-flavor system is (μ_B^c = 0.74 GeV, T^c = 0.094 GeV). These results are consistent with other non-perturbative models such as DSE-FRG, FRG, and the extended DGR model. The predicted CEP for the 2+1-flavor system is close to recent results from these models. The study shows that the EMD framework with machine learning provides a robust description of QCD matter at finite temperature and chemical potential. The results suggest that dynamic quarks influence the location of the CEP. This work represents the first attempt to construct an analytical holographic model using machine learning, offering insights into the QCD phase diagram and hadron spectra. Future work aims to incorporate more information into the holographic QCD model to make it more realistic.
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