From Vacuum to Nucleon: Exact Fixed-Scale Matching of Holographic Current Correlators to QCD

TL;DR

This paper establishes an exact fixed-scale holographic matching for hadronic current correlators in QCD, extending vacuum results to off-forward processes like DDVCS/DVCS, and connects holographic amplitudes with perturbative QCD Wilson coefficients.

Contribution

It provides a novel exact fixed-scale matching framework for holographic current correlators, including off-forward processes, bridging holography and perturbative QCD in a precise way.

Findings

Holographic vacuum matching extends to off-forward correlators.

Derived a universal, model-independent holographic Compton amplitude.

Exact kernel matches perturbative QCD Wilson coefficients at a fixed scale.

Abstract

Holographic QCD reproduces the leading short-distance vector-current two-point function in vacuum, fixing the bulk gauge coupling by matching the logarithmic $Q^2$ dependence of the boundary current correlator. We show that this vacuum matching extends to the off-forward hadronic current-current correlator relevant for DDVCS/DVCS. Starting from the fixed-$j$ $t$-channel Witten diagram, we derive a factorized holographic Compton amplitude whose ultraviolet photon vertex is universal and model independent, while all infrared sensitivity is isolated in hadronic conformal moments. In the conformal limit this upper vertex depends only on the pure-AdS bulk wave functions of the virtual photons and yields an exact Gauss hypergeometric kernel. In the collinear window and at a single matching scale $Q=\mu=\mu_0=\mu_\ast$, this kernel matches exactly the $\pm$-basis Wilson coefficients of the singlet conformal operator product expansion in perturbative QCD. The channel dictionary is fixed dynamically: the closed-string branch matches the protected $(-)$ eigenchannel, while the open-string branch matches the unprotected $(+)$ eigenchannel, with the first physical even moment $j=2$ and the distinct $\sqrt{j-2}$ versus $\sqrt{j-1}$ branch points providing the sharpest anchor. The result is therefore an exact fixed-scale matching statement for the hadronic current-current correlator in the fixed-$j$ channel. It identifies the holographic DDVCS/DVCS amplitude as a hadronic generalization of the familiar vacuum current-correlator matching.