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

Abstract

In this paper, we investigate QCD-like running coupling αsAdS (Q2) and its associated β-function β(Q2) in the spirit of tachyonic AdS/QCD. We distort the bulk AdS5 space using color dielectric function G(ϕ(z)) associated with tachyons, with ϕ(z) the tachyon field. The function presents different properties of αsAdS (Q2) at small and large values of the fifth-dimensional holographic variable z. The function distorts the AdS space, giving αsAdS (Q2) and its β-function β(Q2) at any Q2 scale, with Q2 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 αsAdS (Q2) and its β(Q2) in both the ultraviolet (UV) and infrared (IR) regions using a single function in the framework of tachyonic AdS/QCD.