Holographic CBK Relation

TL;DR

This paper investigates the Crewther-Broadhurst-Kataev (CBK) relation in QCD using holographic duality, confirming perturbative validity at high momenta and analyzing non-perturbative effects at low momenta.

Contribution

It provides a holographic framework to study non-perturbative corrections to the CBK relation and derives exact expressions for related QCD functions.

Findings

Perturbative CBK relation holds at large momenta.

Non-perturbative corrections significantly affect the relation at small momenta.

Derived holographic expressions for the Bjorken function and three-point correlator.

Abstract

The Crewther-Broadhurst-Kataev (CBK) relation connects the Bjorken function for deep-inelastic sum rules (or the Gross - Llewellyn Smith function) with the Adler function for electron-positron annihilation in QCD; it has been checked to hold up to four loops in perturbation theory. Here we study non-perturbative terms in the CBK relation using a holographic dual theory that is believed to capture properties of QCD. We show that for the large invariant momenta the perturbative CBK relation is exactly satisfied. For the small momenta non-perturbative corrections enter the relation and we calculate their significant effects. We also give an exact holographic expression for the Bjorken function, as well as for the entire three-point axial-vector-vector correlation function, and check their consistency in the conformal limit.