From Vacuum to Nucleon: Fixed-$j$ Kernel Matching of Holographic Current Correlators to QCD

Abstract

We show that the normalized non-normalizable photon profile fixed by the vacuum vector-current two-point function, when inserted into the fixed-$j$ hadronic Witten diagram, produces the fixed-$j$ conformal hard kernel in the leading-twist singlet vector channel of deeply virtual Compton scattering (DVCS) and double deeply virtual Compton scattering (DDVCS). For the near-boundary Brower--Polchinski--Strassler--Tan closed-string upper vertex, the Witten diagram yields the Gauss-hypergeometric Wilson-kernel family of the QCD conformal OPE, with the Mellin exponent derived from the explicit $z$-power count $δ_c(j)=j+Δ_c(j)-2$, not inserted as an ansatz. The lower Witten vertex is matched to, or provides a holographic representation of, the nonperturbative conformal moment; it is not a new hard kernel or a freely adjustable skewness profile. The matching is TT-projected, kernel-level, and fixed-scale in the conformal partial-wave/CS representation: finite coefficient normalizations, spin-$j$ source normalizations, scale factors, and lower hadronic matrix elements remain matched inputs. Together with the Nishio--Watari open branch and the protected/unprotected $j=2$ split, this structurally identifies the protected closed branch with the $(-)$ conformal partial wave and the even open branch with the unprotected $(+)$ counterpart in the projected fixed-$j$ singlet vector amplitude; these are mixed singlet eigenchannels, not literal unmixed quark/gluon operators at finite $N_c$. The conformal/Gegenbauer basis used in generalized parton distribution (GPD) deconvolution therefore has a second ultraviolet origin: it is selected both by the QCD OPE and by the near-boundary AdS Witten vertex.