Learning holographic QCD with unflavored meson spectra

A

bstract

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 , a ₁ , a ₂ , and f ₀ 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 ) ∼ k ₁ X ³ + k ₂ X ⁴ , was computed, and the parameters k ₁ and k ₂ 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.