The beta-function of the Wess-Zumino model at O(1/N^2)

TL;DR

This paper extends a method to compute the beta-function of the Wess-Zumino model at large N, revealing higher order corrections' impact on the convergence and critical exponents in supersymmetric field theories.

Contribution

It introduces a superfield extension of the critical point method and calculates the beta-function and critical exponents of the Wess-Zumino model at O(1/N^2).

Findings

Higher order corrections affect the radius of convergence of the beta-function.

Critical exponent matches that of the supersymmetric O(N) sigma model.

Non-renormalization theorem limits critical point equivalence.

Abstract

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 4-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/N^2) 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.