QCD Running Coupling in the Nonperturbative and Near-Perturbative Regimes.

We use analytic continuation to extend the gauge-gravity duality nonperturbative description of the strong force coupling into the transition, near-perturbative, regime where perturbative effects become important. By excluding the unphysical region in coupling space from the flow of singularities in the complex plane, we derive a specific relation between the scales relevant at large and short distances; this relation is uniquely fixed by requiring maximal analyticity. The unified effective coupling model gives an accurate description of the data in the nonperturbative and the near-perturbative regions.