TTP10-05 Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^$ in a General Gauge Theory

We compute, for the first time, the order alpha_s^4 contributions to the Bjorken sum rule for polarized electron-nucleon scattering and to the (non-singlet) Adler function for the case of a generic colour gauge group. We confirm at the same order a (generalized) Crewther relation which provides a strong test of the correctness of our previously obtained results: the QCD Adler function and the five-loop \beta-function in quenched QED. In particular, the appearance of an irrational contribution proportional to zeta_3 in the latter quantity is confirmed. We obtain the {\em commensurate} scale equation relating the effective strong coupling constants as inferred from the Bjorken sum rule and from the Adler function at order alpha_s^4.