The two-loop β-function in models with extended rigid supersymmetry

The two-loop propagators and β-function of a general N =2 supersymmetric model comprising N = 2 Yang-Mills coupled to sets of N = 2 hypermultiplets are calculated by N = 1 supergraph techniques. It is shown that all such models are finite at two loops while a subset is also finite at the one-loop level. The calculation thus confirms the finiteness theorems, and shows that they are valid at the two-loop level even if the hypermultiplet is in a complex representation of the gauge group.