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

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.

10 latex pages, 5 postscript figures

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• Unknotting the polarized vacuum of quenched QED
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Cited by in corpus (6)

• The F-Theorem and F-Maximization
• A 3d disordered superconformal fixed point
• Bootstrapping $O(N)$ Vector Models with Four Supercharges in $3\le d\le 4$
• Critical Wess-Zumino models with four supercharges from the functional renormalization group
• The beta-function of the Wess-Zumino model at O(1/N^2)
• Five loop renormalization of the Wess-Zumino model