Machine learning holographic black hole from lattice QCD equation of state
Xun Chen, Mei Huang
Abstract
Based on lattice QCD results of equation of state and baryon number susceptibility at zero baryon chemical potential, and supplemented by machine learning techniques, we construct the analytic form of the holographic black hole metric in the Einstein-Maxwell-Dilaton framework for pure gluon, 2-flavor, and (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>2</a:mn><a:mo>+</a:mo><a:mn>1</a:mn></a:mrow></a:math>)-flavor systems, respectively. The dilaton potentials solved from Einstein equations are in good agreement with the extended nonconformal DeWolfe-Gubser-Rosen type dilaton potentials fixed by lattice QCD equation of state, which indicates the robustness of the Einstein-Maxwell-Dilaton framework. The predicted critical end point in the (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mn>2</c:mn><c:mo>+</c:mo><c:mn>1</c:mn></c:mrow></c:math>)-flavor system is located at (<e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:msup><e:mrow><e:mi>T</e:mi></e:mrow><e:mrow><e:mi>c</e:mi></e:mrow></e:msup><e:mo>=</e:mo><e:mn>0.094</e:mn><e:mtext> </e:mtext><e:mtext> </e:mtext><e:mi>GeV</e:mi></e:mrow></e:math>, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msubsup><g:mi>μ</g:mi><g:mi>B</g:mi><g:mi>c</g:mi></g:msubsup><g:mo>=</g:mo><g:mn>0.74</g:mn><g:mtext> </g:mtext><g:mtext> </g:mtext><g:mi>GeV</g:mi></g:math>), which is close to the results from the realistic Polyakov-Nambu-Jona-Lasinio model, the functional renormalization group, and the holographic model with extended DeWolfe-Gubser-Rosen dilaton potential. Published by the American Physical Society 2024