  Conformal symmetry-based relations between concrete perturbative QED and QCD
approximations for the Bjorken, the Ellis-Jaffe sum rules of polarized lepton-
nucleon deep-inelastic scattering (DIS), the Gross-Llewellyn Smith sum rules of
neutrino-nucleon DIS, and for the Adler functions of axial-vector and vector
channels are derived. They result from the application of the operator product
expansion to three triangle Green functions, constructed from the non-singlet
axial-vector, and two vector currents, the singlet axial-vector and two
non-singlet vector currents and the non-singlet axial-vector, vector and
singlet vector currents in the limit, when the conformal symmetry of the gauge
models with fermions is considered unbroken. We specify the perturbative
conditions 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 the
conformal invariant limit between the concrete contributions to the Bjorken,
the Ellis-Jaffe and the Gross-Llewellyn Smith sum rules is proved. The
analytical and numerical $O(\alpha^4)$ and $O(\alpha_s^2)$ conformal symmetry
based approximations for these sum rules and for the Adler function of the
non-singlet vector currents are summarized. Possible theoretical applications
of the results presented are discussed.
