On the D=4, N=2 non-renormalization theorem

Using the harmonic superspace background field formulation for general D = 4, N = 2 super Yang-Mills theories, with matter hypermultiplets in arbitrary representations of the gauge group, we present the first rigorous proof of the N=2 non-renormalization theorem; specifically: the absence of ultraviolet divergences beyond the one-loop level, Another simple consequence of the background field formulation is the absence of the leading non-holomorphic correction to the low-energy effective action at two loops. (C) 1998 Published by Elsevier Science B.V. All rights reserved.