Deriving the dilaton potential in improved holographic QCD from the chiral condensate

We derive an explicit form of the dilaton potential in improved holographic QCD (IHQCD) from the QCD lattice data of the chiral condensate as a function of the quark mass. This establishes a data-driven holographic modeling of QCD-machine-learning holographic QCD. The modeling consists of two steps for solving inverse problems. The first inverse problem is to find the emergent bulk geometry consistent with the lattice QCD simulation data at the boundary. We solve this problem with the refinement of the neural ordinary differential equation, a machine-learning technique. The second inverse problem is to derive a bulk gravity action with a dilaton potential such that its solution is the emergent bulk geometry. We solve this problem at non-zero temperature, and derive the explicit form of the dilaton potential. The dilaton potential determines the bulk action, the Einstein-dilaton system; thus we derive holographically the bulk system from the QCD chiral condensate data. The usefulness of the model is shown in the example of the prediction of the string breaking distance, whose value is found to be consistent with other lattice QCD data.