  Establishing an explicit connection between the long distance physics of
confinement and the dynamical interactions of quarks and gluons at short
distances has been a long-sought goal of quantum chromodynamics. Using
holographic QCD, we derive a direct analytic relation between the scale
$\kappa$ which determines the masses of hadrons and the scale $\Lambda_{s}$
which controls the predictions of perturbative QCD at very short distances. The
resulting prediction $\Lambda_{s}=0.341\pm0.032$ GeV in the $\overline{MS}$
scheme agrees well with the experimental average $0.339\pm0.016$ GeV. We also
derive a relation between $\Lambda_{s}$ and the QCD string tension $\sigma$.
This connection between the fundamental hadronic scale underlying the physics
of quark confinement and the perturbative QCD scale controlling hard collisions
can be carried out in any renormalization scheme.
