Tachyonic AdS/QCD, Determining the Strong Running Coupling and β-Function in Both UV and IR Regions of AdS Space

In this paper, we investigate the Quantum Chromodynamics (QCD)-like running coupling, αsAdS(Q2), and its associated β-function within a tachyonic Anti-de Sitter (AdS)/QCD framework. The AdS5 bulk geometry is deformed through the introduction of a color dielectric function G(ϕ(z)), associated with a tachyon field ϕ(z). This function governs the behavior of αsAdS(Q2) across all momentum scales by modifying the AdS background at both small and large values of the holographic coordinate z. In the ultraviolet (UV) regime (small z), the deformation is driven by free tachyons and reproduces features consistent with perturbative QCD. In contrast, in the infrared (IR) regime (large z), tachyon condensation dominates, yielding behavior characteristic of nonperturbative QCD. This construction enables a unified description of the running coupling and its β-function over the full range of momentum transfer Q2, where Q2 denotes the space-like momentum scale.