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  • Open Access

Data-driven Einstein-dilaton model for pure Yang-Mills thermodynamics and glueball spectrum

Xun Chen1,2,*, Yidian Chen3,†, and Kai Zhou4,5,‡

  • *Contact author: chenxun@usc.edu.cn
  • †Contact author: chenyidian@hznu.edu.cn
  • ‡Contact author: zhoukai@cuhk.edu.cn
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Phys. Rev. D 112, 126025 – Published 26 December, 2025

DOI: https://doi.org/10.1103/wyr3-2kc5

Abstract

We develop a machine learning assisted holographic model that consistently describes both the equation of state and glueball spectrum of pure Yang-Mills theory, achieved through neural network reconstruction of Einstein-dilaton gravity. Our framework incorporates key nonperturbative constraints of lattice QCD data: The ground (0++) and first-excited (0++*) scalar glueball masses pins down the infrared (IR) geometry, while entropy density data anchors the ultraviolet (UV) behavior of the metric. A multistage neural network optimization then yields the full gravitational dual—warp factor A(z) and dilaton field Φ(z)—that satisfies both spectroscopic and thermodynamic constraints. The resulting model accurately reproduces the deconfinement phase transition thermodynamics (pressure, energy density, trace anomaly) and predicts higher glueball excitations (0++**, 0++***) consistent with available lattice calculations. This work establishes a new paradigm for data-driven holographic reconstruction, solving the long-standing challenge of unified description of confinement thermodynamics and spectroscopy.

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Phys. Rev. D 112, 126025– Published 26 December, 2025
  • Received 29 September 2025
  • Accepted 5 December 2025
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