Confinement Potential in a Soft-Wall Holographic Model with a Hydrogen-like Spectrum

It is well known that the Soft-Wall holographic model for QCD successfully reproduces not only linear Regge spectrum, but also, via Wilson confinement criterion, ''linear plus Coulomb'' potential similar to Cornell potential. This property could be interpreted as a counterpart of hadron string picture, where linearly rising and Regge-like spectrum are directly related. However, such relation does take place in bottom-up approach. Namely, Cornell-like potentials arise broad class models, standard merely particular representative this class. We consider calculation within different - with dilaton background metric. leads Hydrogen like spectrum. The renormalized at short distances turns out complicated by new subtlety was skipped general discussions issue existing literature. But shown very from obtained quadratic background.