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Conformal symmetry-based relations between concrete perturbative QED and QCDapproximations for the Bjorken, the Ellis-Jaffe sum rules of polarized lepton-nucleon deep-inelastic scattering (DIS), the Gross-Llewellyn Smith sum rules ofneutrino-nucleon DIS, and for the Adler functions of axial-vector and vectorchannels are derived. They result from the application of the operator productexpansion to three triangle Green functions, constructed from the non-singletaxial-vector, and two vector currents, the singlet axial-vector and twonon-singlet vector currents and the non-singlet axial-vector, vector andsinglet vector currents in the limit, when the conformal symmetry of the gaugemodels with fermions is considered unbroken. We specify the perturbativeconditions for this symmetry to be valid in the case of the $U(1)$ and$SU(N_c)$ models. The all-order perturbative identity following from theconformal invariant limit between the concrete contributions to the Bjorken,the Ellis-Jaffe and the Gross-Llewellyn Smith sum rules is proved. Theanalytical and numerical $O(\alpha^4)$ and $O(\alpha_s^2)$ conformal symmetrybased approximations for these sum rules and for the Adler function of thenon-singlet vector currents are summarized. Possible theoretical applicationsof the results presented are discussed.

Conformal symmetry limit of QED and QCD and identities between perturbative contributions to deep-inelastic scattering sum rules