Emergence of confinement and limits of applicability of holographic QCD: Analytic amplitudes at all scales

Virtuality and coherence determine the limits of applicability of holographic concepts in QCD.In light-front quantization, the invariant mass controls the off-shell behavior of a physical process and thus provides a measure of its virtuality.In impact space, the corresponding quantity is the invariant transverse separation between quarks and gluons, , which is identified with the holographic coordinate in holographic light-front QCD.By embedding the internal structure of hadrons and implementing an effective superconformal symmetry, the mapping between quantum states and classical gravity -central to the holographic principle-yields new analytic insights into the strong-interaction dynamics responsible for the emergence of a confinement scale and the observed hadron spectrum.We show that the possible emergence of a gravity dual to physical QCD is restricted to the Regge limit of high-energy scattering, where many partonic degrees of freedom participate coherently.This criterion provides a quantitative definition of the domain of applicability of holographic QCD to dynamical processes and allows it to be tested directly against experimental results.By further enforcing analyticity together with exact QCD constraints at asymptotic infinity, the holographic framework can be consistently extended beyond the infrared domain.To illustrate this procedure, we briefly discuss recent work by the HLFHS collaboration, where the effective strong coupling was extended from the Regge-limit domain, through the near-perturbative transition region, and into the ultraviolet Bjorken-limit domain.The resulting scheme provides a unified and precise nonperturbative description of the strong coupling across all virtuality scales."High-energy scattering and deep inelastic processes are two aspects of the same amplitude, connected through virtuality and coherence."