The one-loop effective super-potential and non-holomorphicity

We calculate the Kählerian and the lowest order non-Kählerian contributions to the one-loop effective superpotential using super-Feynman graphs in the massless Wess-Zumino model, the massive Wess-Zumino model and N = 1, U(I) gauge theory. We also calculate the Kählerian term in Yang-Mills theory for a general gauge group. Using this latter result we find the one-loop Kählerian contribution for N = 2 Yang-Mills theory in terms of N = 1 superfields and we show that it can only come from non-holomorphic contributions to the N = 2 effective potential.