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<p>We develop a data-driven neural network framework to reconstruct the five-dimensional background geometry, the dilaton potential, and the chiral-symmetry-breaking scalar potential of holographic QCD from hadron mass spectra. Framed as an inverse problem, the model is trained using a discretized form of the Schrödinger-like equation, which resembles a linear moose in “deconstructed” 5 dimensions with Dirichlet boundary conditions, in contrast to the AdS/DL with “emergent” space-time. Using the masses of the unflavored mesons <i>ρ</i>, <i>a</i><sub>1</sub>, <i>a</i><sub>2</sub>, and <i>f</i><sub>0</sub> and their excitations as training data, the model learns confining effective potentials and computes a dilaton profile that satisfies the null energy condition. The network predicts that the dilaton’s IR behavior will be much steeper than its quadratic form. Moreover, the symmetry-breaking bulk potential of the scalar field, <i>V</i> (<i>X</i>) ∼ <i>k</i><sub>1</sub><i>X</i><sup>3</sup> + <i>k</i><sub>2</sub><i>X</i><sup>4</sup>, was computed, and the parameters <i>k</i><sub>1</sub> and <i>k</i><sub>2</sub> predicted to be ~ –4 and ~ 9 respectively. The deep-learned parameters, metric, and the dilaton profile were then used to predict the pion mass and its spectrum with good accuracy. A Python code, along with the trained models, is provided to facilitate further studies.</p>

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Learning holographic QCD with unflavored meson spectra

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月22日

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  • Mathew Thomas Arun,
  • Ritik Pal

摘要

We develop a data-driven neural network framework to reconstruct the five-dimensional background geometry, the dilaton potential, and the chiral-symmetry-breaking scalar potential of holographic QCD from hadron mass spectra. Framed as an inverse problem, the model is trained using a discretized form of the Schrödinger-like equation, which resembles a linear moose in “deconstructed” 5 dimensions with Dirichlet boundary conditions, in contrast to the AdS/DL with “emergent” space-time. Using the masses of the unflavored mesons ρ, a1, a2, and f0 and their excitations as training data, the model learns confining effective potentials and computes a dilaton profile that satisfies the null energy condition. The network predicts that the dilaton’s IR behavior will be much steeper than its quadratic form. Moreover, the symmetry-breaking bulk potential of the scalar field, V (X) ∼ k1X3 + k2X4, was computed, and the parameters k1 and k2 predicted to be ~ –4 and ~ 9 respectively. The deep-learned parameters, metric, and the dilaton profile were then used to predict the pion mass and its spectrum with good accuracy. A Python code, along with the trained models, is provided to facilitate further studies.