Adler Function, DIS sum rules and Crewther Relations

Abstract: The current status of the Adler function and two closely related Deep Inelastic Scattering (DIS) sum rules, namely, the Bjorken sum rule for polarized DIS and the Gross-Llewellyn Smith sum rule are briefly reviewed. A new result is presented: an analytical calculation of the coefficient function of the latter sum rule in a generic gauge theory in order O(alpha_s^4). It is demonstrated that the corresponding Crewther relation allows to fix two of three colour structures in the O(alpha_s^4) contribution to the singlet part of the Adler function.