We use the functional form of the QCD running coupling to modify the conformal metric in AdS/CFT mapping the fifth-dimensional z-coordinate to the energy scale in the four-dimensional QCD. The resulting type-0 string theory in five dimensions is solved with the Nambu-Goto action giving good agreement with the Coulombic and confinement QQ potential.

We construct the dilaton potential in the gravity dual theory of AdS/QCD for the warp factor of Refs. [1,2]. Using this AdS 5 -metric with properties similar to QCD, we find that the gravity dual leads to a meaningful gauge coupling in the region between the charmonium and bottonium mass, but differs slightly from QCD in the extreme UV. When we fix the ultraviolet behavior in accord with the β-function, we can obtain good agreement with the overall heavy quark-antiquark potential. Although the leading order proportional to − α 4/3 r differs from perturbative QCD, the full potential agrees quite well with the short distance QCD potential in NNLO.

We use the vacuum expectation value of a Wegner-Wilson loop representing a fast moving quarkantiquark pair to derive the light cone Hamiltonian for a qq meson. We solve the corresponding Schrödinger equation for various trial wave functions. The result shows how confinement determines the meson mass and wave function for valence quarks on the light cone. We also parametrize the effect of the spin-dependent splitting for a light meson and charmonium. The correct chiral-symmetry breaking pattern for the pion mass is obtained due to the self-energy of the quark.

The vacuum expectation value of a Wegner-Wilson loop representing a fast moving quarkantiquark pair defines the light-cone Hamiltonian for a qq meson. We solve the corresponding Schrödinger equation for various trial wave functions. The result shows how confinement determines the light-cone wave function for valence quarks in a rather model-independent way. The correct chiral-symmetry behavior of the pion mass is obtained when the self-energy of the quark is chosen properly.