Deriving the dilaton potential in improved holographic QCD from the meson spectrum

We derive an explicit form of the dilaton potential in improved holographic QCD (IHQCD) from the experimental data of the meson spectrum. For this purpose, we make use of the emergent bulk geometry obtained by deep learning from the hadronic data in the work by Akutagawa et al. Phys. Rev. D 102, 026020 (2020). Requiring that the geometry is a solution of an IHQCD derives the corresponding dilaton potential backward. This determines the bulk action in a data-driven way, which enables us at the same time to ensure that the deep learning proposal is a consistent gravity. Furthermore, we find that the resulting potential satisfies the requirements normally imposed in IHQCD, and that the holographic Wilson loop for the derived model exhibits quark confinement.