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.

arXiv comment16 latex pages, 4 figures; v2: comments and references added; a remark about Schwinger's paper corrected; to appear in PLB

References in corpus (20)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• QCD and a Holographic Model of Hadrons
• Chiral symmetry breaking from five dimensional spaces
• More on a holographic dual of QCD
• QCD at Low Energies
• The Uses of Conformal Symmetry in QCD
• Connections between Deep-Inelastic and Annihilation Processes at Next-to-Next-to-Leading Order and Beyond
• Form Factors and Wave Functions of Vector Mesons in Holographic QCD
• Baryon Number-Induced Chern-Simons Couplings of Vector and Axial-Vector Mesons in Holographic QCD
• Adler Function, Sum Rules and Crewther Relation of Order O(alpha_s^4): the Singlet Case
• The Generalized Crewther Relation in QCD and its Experimental Consequences
• Relating inclusive e+e- annihilation to electroproduction sum rules in Quantum Chromodynamics
• Explicit Results for the Anomalous Three Point Function and Non-Renormalization Theorems
• New perturbation theory representation of the conformal symmetry breaking effects in gauge quantum field theory models
• Anomalous $A{V}^{\ast }V$ vertex function in the soft-wall holographic model of QCD
• Photoproduction through Chern-Simons Term Induced Interactions in Holographic QCD
• Adler function and Bjorken polarized sum rule: Perturbation expansions in powers of $SU(N_c)$ conformal anomaly and studies of the conformal symmetry limit
• The VVA correlator at three loops in perturbative QCD
• On Connection between Coefficient Functions for Deep-Inelastic and Annihilation Processes

Cited by in corpus (1)

• Parity-Odd 3-Point Functions from CFT in Momentum Space and the Chiral Anomaly