NON-ZETA KNOTS IN THE RENORMALIZATION OF THE WESS-ZUMINO MODEL

We solve the Schwinger Dyson equations of the O(N) symmetric Wess-Zumi no model at O(1/N-3) at the non-trivia] fixed point of the d-dimension al beta-function and deduce a critical exponent for the wave function renormalization at this order. By developing the epsilon-expansion of the result, which agrees with known perturbation theory, we examine th e distribution of transcendental coefficients and show that only the R iemann zeta series arises at this order in 1/N. Unlike the analogous c alculation at the same order in the bosonic O(N) phi(4)-theory non-zet a transcendentals, associated with for example the (3,3)-torus knot, c ancel. (C) 1998 Elsevier Science B.V.