Asymptotic gauge symmetry and UV extension of the nonperturbative coupling in holographic QCD

We extend our recent analytic study of the strong coupling ${\ensuremath{\alpha}}_{\mathrm{eff}}$ in the nonperturbative and near-perturbative regimes [Phys. Rev. Lett. 133, 181901 (2024)] by imposing rigorous renormalization-group constraints from asymptotically free gauge theories at ${Q}^{2}\ensuremath{\rightarrow}\ensuremath{\infty}$. The asymptotic boundary conditions modify the scaling properties of ${\ensuremath{\alpha}}_{\mathrm{eff}}$ at large values of the momentum transfer ${Q}^{2}$ and lead to a scale-dependent confinement strength $\ensuremath{\kappa}({Q}^{2})$. This requires that both $\ensuremath{\kappa}({Q}^{2})$ and ${\ensuremath{\alpha}}_{\mathrm{eff}}({Q}^{2},\ensuremath{\kappa}({Q}^{2}))$ remain holomorphic in the complex ${Q}^{2}$ plane, except at the physical cuts associated with the heavy-quark thresholds and the singularity flow trajectory studied in our previous Letter. For color SU(3), a precise connection is found between the scaling exponent of $\ensuremath{\kappa}({Q}^{2})$ in the ultraviolet, the value of the infrared fixed point of the strong coupling, and the number of flavors in agreement with observations. The nonperturbative analytic model gives an accurate description of the strong coupling across all scales, up to the highest available data.