Holographic QCD equation of state constrained by lattice QCD: neural-ODE for probe-limit and a back-reaction test

TL;DR

This paper develops a neural-ODE based holographic QCD model calibrated with lattice QCD data, exploring probe-limit and back-reaction effects to understand the equation of state of QCD matter.

Contribution

It introduces a neural network approach to reconstruct holographic model functions and tests back-reaction effects, advancing the modeling of QCD thermodynamics.

Findings

Neural-ODE framework effectively calibrates holographic models to lattice QCD data.

Back-reaction causes a mismatch with pure-glue results at finite temperature.

High-temperature ratios approach a pure-glue baseline, indicating flavor-sector truncation effects.

Abstract

We study the equation of state (EoS) of QCD matter in a bottom-up holographic setup that combines an Einstein-Maxwell-dilaton (EMD) sector with an improved Karch-Katz-Son-Stephanov (KKSS) flavor action. In the probe approximation, we perform an inverse reconstruction of the model functions by parameterizing them with neural networks and solving the EMD equations via a differentiable ODE solver (a neural ODE framework), calibrating the model to a $(2+1)$-flavor lattice-QCD EoS at finite temperature and finite baryon chemical potential. The reconstructed model functions are then parametrized and kept fixed across thermodynamic states. Next, viewing the EMD sector as an effective description of pure Yang--Mills theory, we fix its parameters by fitting the $\mu_B=0$ lattice pure-glue EoS using a hybrid optimization strategy. Finally, we go beyond the probe limit and solve the coupled EMD$+$KKSS equations with back-reaction, using the pure-glue-calibrated EMD sector as a fixed input and varying the KKSS couplings to compare with the $\mu_B=0$ two-flavor lattice EoS. We find a visible mismatch and a high-temperature behavior in which the back-reacted dimensionless ratios approach a nearly $\beta_1$-insensitive plateau close to the pure-glue baseline, providing a simple structural diagnostic for the present flavor-sector truncation.