Riemann $\zeta (3)$- terms in perturbative QED series, conformal symmetry and the analogies with structures of multiloop effects in N=4 supersymmetric Yang-Mills theory

Abstract

As was discovered recently, 5-loop perturbative quenched QED approximation to the QED $\beta$-function consist from the rational term and the term proportional to $\zeta (3)$-function. It is stressed, that this feature is also manifesting itself in the conformal invariant pqQED series for the 4-loop approximation to the anomalous mass dimension. The 4-loop pqQED expression for the singlet contribution into the Ellis-Jaffe polarized sum rule is obtained. It coincides with the similar approximation for the non-singlet coefficient function of Ellis-Jaffe sum rule and of Bjorken polarized sum rule. It is stressed that this property is valid in all orders of perturbation theory thanks to the conformal symmetry of pqQED series and to Crewther relation, which relates non-singlet and singlet coefficient functions of Ellis-Jaffe sum rule with the coefficient functions of non-singlet and singlet Adler D-functions. The basic steps of derivation of Crewther relation in the singlet channel from the AVV triangle diagram are outlined. The similarities between analytical structure of asymptotic series for the coefficient functions in pqQED and for the anomalous dimensions in N=4 conformal invariant supersymmetric Yang-Mills theory are observed. The guess is proposed that the appearance of $\zeta (3)$-terms in the pqQED expressions and the absence of $\zeta (5)$-terms at the same level is the indication of absence of "wrapping" interactions in pqQED.

arXiv commentAccepted to Phys.Lett.B , 2 more references added after acception without modifying the text

References in corpus (29)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Bethe Ansatz for Quantum Strings
• The 4-loop quark mass anomalous dimension and the invariant quark mass
• The renormalization of the axial anomaly in dimensional regularization
• Three-loop universal anomalous dimension of the Wilson operators in N=4 SUSY Yang-Mills model
• Quark Mass Anomalous Dimension to alpha_s**4
• Wrapping interactions and a new source of corrections to the spin-chain/string duality
• Quark and gluon form factors to three loops
• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^4 in a General Gauge Theory
• Dressing and Wrapping
• Connections between Deep-Inelastic and Annihilation Processes at Next-to-Next-to-Leading Order and Beyond
• Five-Loop Anomalous Dimension of Twist-Two Operators
• Five loop Konishi from AdS/CFT
• Anomalous dimension with wrapping at four loops in N=4 SYM
• The Four-Loop Konishi in N=4 SYM
• Analytical on-shell QED results: 3-loop vacuum polarization, 4-loop beta-function and the muon anomaly
• The (alpha_s)^3 approximation of Quantum Chromodynamics to the Ellis-Jaffe sum rule
• Unknotting the polarized vacuum of quenched QED
• Relating inclusive e+e- annihilation to electroproduction sum rules in Quantum Chromodynamics
• Five-loop anomalous dimension at critical wrapping order in N=4 SYM
• Analytic solution of the multiloop Baxter equation
• Leading transcedental contribution to the four-loop universal anomalous dimension in N=4 SYM
• Four-loop Dyson-Schwinger-Johnson anatomy
• Is it possible to check urgently the 5-loop analytical results for the $e^{+}{e}^{-}$-annihilation Adler function ?
• On Connection between Coefficient Functions for Deep-Inelastic and Annihilation Processes
• Baxter equation beyond wrapping
• Fermionic correlators and zero-momentum modes in quenched lattice QED

Cited by in corpus (11)

• Eliminating the Renormalization Scale Ambiguity for Top-Pair Production Using the Principle of Maximum Conformality
• The Renormalization Scale-Setting Problem in QCD
• Renormalization Group Invariance and Optimal QCD Renormalization Scale-Setting
• NSVZ scheme with the higher derivative regularization for N=1 SQED
• Self-Consistency Requirements of the Renormalization Group for Setting the Renormalization Scale
• New perturbation theory representation of the conformal symmetry breaking effects in gauge quantum field theory models
• The Adler $D$-function for $\mathcal{N}=1$ SQCD regularized by higher covariant derivatives in the three-loop approximation
• Finite remainders of the Konishi at two loops in $\mathcal{N}=4$ SYM
• Conformal symmetry limit of QED and QCD and identities between perturbative contributions to deep-inelastic scattering sum rules
• The analytical singlet ${\alpha }_s^4$ QCD contributions into the $e^{+}{e}^{-}$-annihilation Adler function and the generalized Crewther relations
• Superspace methods for the computation of wrapping effects in the standard and beta-deformed N=4 SYM