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  • Open Access

Toward a unified Einstein-Maxwell-dilaton framework of QCD

Hong-An Zeng*

Lingxiao Wang†

Mei Huang‡

  • Center for Theoretical Physics and College of Physics, Jilin University, Changchun 130012, China

  • *Contact author: zengha20@mails.jlu.edu.cn
  • †Contact author: lingxiao.wang@riken.jp
  • ‡Contact author: huangmei@ucas.ac.cn
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Phys. Rev. D 113, 126001 – Published 2 June, 2026

DOI: https://doi.org/10.1103/cdts-qpvn

Abstract

We propose HoloNet, a neural-network framework that unifies lattice QCD (LQCD) thermodynamics and holographic Einstein-Maxwell-Dilaton (EMD) theory within a data-to-holography pipeline. Instead of assuming specific functional forms, HoloNet learns the metric profile A(z) and the gauge-dilaton coupling f(z) directly from 2+1-flavor LQCD data at μ=0. These learned functions are embedded into the EMD equations, enabling the model to reproduce the lattice equation of state and baryon number fluctuations with high fidelity. Once trained, HoloNet provides a fully data-driven holographic description of QCD that extends naturally to finite density, allowing us to map the phase diagram and estimate the location of the critical end point. The reconstructed potential V(ϕ) and coupling f(ϕ) agree quantitatively with those obtained from holographic renormalization, demonstrating that HoloNet can consistently bridge different holographic models.

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Phys. Rev. D 113, 126001– Published 2 June, 2026
  • Received 15 December 2025
  • Accepted 23 April 2026
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