Data-Driven Einstein-Dilaton Model for Pure Yang-Mills Thermodynamics and Glueball Spectrum

TL;DR

The paper tackles the problem of simultaneously describing confinement thermodynamics and glueball spectroscopy in pure Yang-Mills theory. It introduces a data-driven, bottom-up holographic approach that reconstructs a self-consistent Einstein–dilaton background from lattice benchmarks using neural networks to determine the warp factor $A(z)$ and dilaton $\Phi(z)$. The method enforces IR constraints from the ground and first excited scalar glueball masses and UV constraints from entropy density $s/T^3$, yielding a dual that reproduces the deconfinement transition and predicts higher glueball excitations in agreement with lattice data. This work provides a quantitative bridge between lattice QCD observables and holographic duals, enabling a unified framework for confinement thermodynamics and spectroscopy with potential extensions to finite density and real-time dynamics.

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 non-perturbative 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 multi-stage 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.

Figures (8)

• Figure 1: The scalar potential $V(\phi)$ as a function of the scalar field $\phi$ in our model at vanishing temperature and chemical potential.
• Figure 2: Comparison between the extracted glueball potential $V_g(z)$ from lattice QCD data and predictions from other holographic QCD models Zhang:2021itx.
• Figure 3: Reconstructed composite derivative $B_P(z) = 3A_s'(z) - \Phi'(z)$ obtained by solving Eq. \ref{['V_g']} using the trained potential $V_g(z)$.
• Figure 4: Final reconstructed warp factor $A(z)$ incorporating entropy and glueball constraints.
• Figure 5: A sketch of holographic reconstruction workflow.