The β-function of the Wess-Zumino model at O(1/N2)

We extend the critical point self-consistency method used to solve field theories at their d-dimensional fixed point in the large N expansion to include superfields. As an application we compute the beta-function of the Wess-Zumino model with an O(N) symmetry to O(1/N-2), This result is then used to study the effect the higher order corrections have on the radius of convergence of the four-dimensional beta-function at this order in 1/N. The critical exponent relating to the wave function renormalization of the basic field is also computed to O(1/N2) and is shown to be the same as that for the corresponding field in the supersymmetric O(N) sigma-model in d dimensions, We discuss how the non-renormalization theorem prevents the full critical point equivalence between both models. (C) 1998 Elsevier Science B.V.