Holographic CBK relation

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.