Adler function, Bjorken Sum Rule and Crewther-Broadhurst-Kataev relation with generic fermion representations at order $O({\alpha }_s^4)$

We compute the nonsinglet Adler $D$-function and the coefficient function for Bjorken polarized sum rules $S^{Bjp}$ at order $O({\alpha }_s^4)$ in an extended QCD model with arbitrary number of fermion representations. The Crewther-Broadhurst-Kataev (CBK) relation in this order is confirmed.