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 QCD-like running coupling α s AdS (Q 2 ) and its associated β- function β(Q 2 ) in the spirit of tachyonic AdS/QCD. We distort the bulk AdS 5 space using color dielectric function G(ϕ(z)) associated with tachyons, with ϕ(z) the tachyon field. The function presents different properties of α s AdS (Q 2 ) at small and large values of the fifth-dimensional holographic variable z . The function distorts the AdS space, giving α s AdS (Q 2 ) and its β -function β(Q 2 ) at any Q 2 scale, with Q 2 the space-like momentum. The result obtained for a large value of z is expected to show characteristics similar to nonperturbative QCD. On the other hand, the result obtained for a small value of z is expected to show characteristics similar to perturbative QCQ. The presence of free tachyons leads to distortion of the AdS space at a small z , that notwithstanding, condensed tachyon states also lead to large z distortion. This provides a unified background for determining α s AdS (Q 2 ) and its β(Q 2 ) in both the ultraviolet (UV) and infrared (IR) regions using a single function in the framework of tachyonic AdS/QCD.