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

TL;DR

This paper develops a holographic QCD model using tachyonic AdS space to unify the description of the strong coupling and $eta$-function across all energy scales, from perturbative to nonperturbative regimes.

Contribution

It introduces a tachyonic deformation of AdS space via a color dielectric function, capturing both UV and IR QCD behaviors in a single holographic framework.

Findings

Reproduces perturbative QCD features in the UV regime.

Models nonperturbative IR behavior through tachyon condensation.

Provides a unified description of the running coupling and $eta$-function.

Abstract

In this paper, we investigate the Quantum Chromodynamics (QCD)-like running coupling, $\alpha_s^{AdS}(Q^{2})$, and its associated $\beta$-function within a tachyonic Anti-de Sitter (AdS)/QCD framework. The $\text{AdS}_5$ bulk geometry is deformed through the introduction of a color dielectric function $G(\phi(z))$, associated with a tachyon field $\phi(z)$. This function governs the behavior of $\alpha_s^{AdS}(Q^{2})$ 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 $\beta$-function over the full range of momentum transfer $Q^2$, where $Q^2$ denotes the space-like momentum scale.