The Crewther relation, schemes, gauges and fixed points

We investigate the Crewther relation at high loop order in a variety of renormalization schemes and gauges. By examining the properties of the relation in schemes other than modified minimal subtraction (MSbar) at the fixed points of Quantum Chromodynamics we propose a generalization of the Crewther relation that extends the MSbar construction of Broadhurst and Kataev. A derivation based on the properties of the renormalization group equation is provided for the generalization which is tested in various scenarios.Comment: 51 latex pages, 10 tables, anc directory contains additional tables and a txt file with the electronic version of results for a general colour group, minor text changes and additional reference