Asymptotic Freedom in SU(3) Yang-Mills Theory within the Simplicial Discrete Informational Spacetime Framework: A Weak Coupling Renormalization Group Analysis

The behavior of quantum Yang-Mills theory across different energy scales, particularly the property of asymptotic freedom at high energies (weak coupling), is fundamental to its consistency with experimental observations in Quantum Chromodynamics (QCD). This paper investigates this high-energy behavior within the theoretical context provided by the Complete Theory of Simplicial Discrete Informational Spacetime (SDIS) (Karazoupis, 2025b). This framework posits a fundamentally discrete, quantum-informational structure for spacetime based on a simplicial network, from which gauge fields emerge via holonomies. Employing analytical Renormalization Group (RG) methods adapted to the SDIS structure (conceptually utilizing techniques like the background field method), the scale dependence of the emergent pure SU(3) gauge coupling is analyzed. It is demonstrated analytically that the beta function for the effective coupling is negative at weak coupling (β < 0). This result confirms that the SDIS framework inherently reproduces asymptotic freedom, the correct ultraviolet behavior of QCD, and allows for the dynamical generation of the physical scale parameter Λ_QCD. This finding, combined with previous results demonstrating a mass gap at strong coupling within SDIS (Karazoupis, 2025c), supports the framework's potential to provide a self-consistent description of Yang-Mills theory across energy scales, resolving incompatibilities present in standard continuum formulations.