Equivalence of the AdS-Metric and the QCD Running Coupling

Understand

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 $Q \bar Q$ potential.