Learning holographic QCD with unflavoured meson spectra

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 Schr\"odinger-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 $\rho$, $a_1$, $a_2$, 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 $\sim -4$ and $\sim 9$ 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\footnote{Available at Github, https://github.com/rp-winter/NN-AdS-QCD}.