Non-zeta knots in the renormalization of the Wess-Zumino model?

TL;DR

This paper computes critical exponents in the O(N) symmetric Wess-Zumino model at high order in 1/N, revealing that only Riemann zeta values appear in the transcendental coefficients, unlike in similar bosonic theories.

Contribution

It provides a detailed high-order calculation of the Wess-Zumino model's critical exponents and uncovers the exclusive appearance of Riemann zeta values in the transcendental coefficients.

Findings

Only Riemann zeta series arise at this order in 1/N.

Non-zeta transcendental numbers cancel out in the calculation.

Results agree with known perturbation theory through epsilon-expansion.

Abstract

We solve the Schwinger Dyson equations of the O(N) symmetric Wess-Zumino model at O(1/N^3) at the non-trivial fixed point of the d-dimensional 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 the distribution of transcendental coefficients and show that only the Riemann zeta series arises at this order in 1/N. Unlike the analogous calculation at the same order in the bosonic O(N) phi^4-theory non-zeta transcendentals, associated with for example the (3,4)-torus knot, cancel.