Holographic Open/Closed Exchange in Double Deeply Virtual Compton Scattering: Fixed--$j$ Structural Matching to the $\pm$-Basis Wilson Coefficients

Abstract: We show that, in the collinear regime, the fixed--$j$ holographic double deeply virtual Compton scattering (DDVCS) amplitude contains the same hypergeometric hard kernel as the $\pm$-basis Wilson coefficients of perturbative QCD. Starting from the $t$--channel Witten diagram, we derive the closed-string fixed--$j$ amplitude and obtain the even-spin open-string channel by a parallel replacement rule. After holographic collinear factorization, the upper photon vertex is universal and model independent: in the conformal limit it depends only on the pure-AdS bulk wave functions of the two virtual photons and yields an exact Gauss hypergeometric function of $η^2/ξ^2$. The Mellin exponent $δX(j)=j+Δ_X(j)-2=2j+γ_X(j)$ is fixed by Witten-diagram $z$-power counting, while all infrared model dependence is isolated in lower hadronic conformal moments. Comparing with the singlet vector Compton form factor in the conformal operator product expansion, we find that at a single matching scale $Q=μ=μ_0=μ\ast$ the open channel matches the $(+)$ eigenchannel and the closed channel matches the protected $(-)$ eigenchannel. The sharpest anchor is the first physical even moment $j=2$, together with the distinct $\sqrt{j-1}$ and $\sqrt{j-2}$ branch-point structure of the open and closed trajectories. Logarithmic running deforms only the scale dependence, not the channel dictionary. The result is a fixed--$j$, fixed-scale structural matching statement for holographic DDVCS/DVCS, not a claim of all-scale equality or a global fit.