Hard-soft renormalization of the massless Wess-Zumino model

TL;DR

This paper demonstrates that in a Wilsonian renormalization scheme with zero-momentum subtraction, the massless Wess-Zumino model adheres to the non-renormalization theorem, providing exact beta and gamma functions and confirming known two-loop results.

Contribution

It establishes the non-renormalization theorem within a Wilsonian scheme and derives exact expressions for beta and gamma functions, confirming their relation and previous two-loop calculations.

Findings

Non-renormalization theorem holds in Wilsonian scheme

Exact beta and gamma functions derived

Two-loop beta function matches previous results

Abstract

We show that in a Wilsonian renormalization scheme with zero-momentum subtraction point the massless Wess-Zumino model satisfies the non-renormalization theorem; the finite renormalization of the superpotential appearing in the usual non-zero momentum subtraction schemes is thus avoided. We give an exact expression of the beta and gamma functions in terms of the Wilsonian effective action; we prove the expected relation $\beta = 3g\gamma$. We compute the beta function at the first two loops, finding agreement with previous results.