Comment about the vanishing of the vacuum energy in the Wess-Zumino model

TL;DR

This paper verifies that the vacuum energy cancels out in the Wess-Zumino model at two-loop order, demonstrating the cancellation mechanisms in different formalisms, thus confirming the model's supersymmetric stability.

Contribution

It provides a detailed two-loop analysis of vacuum energy cancellation in the Wess-Zumino model using different component field formalisms, clarifying the underlying mechanisms.

Findings

Vacuum energy is zero at two-loop order in both formalisms.

Cancellation occurs via different mechanisms depending on auxiliary fields.

Supports the stability of the supersymmetric vacuum.

Abstract

We check the cancellation of the vacuum energy in the Wess-Zumino model at the two-loop order in the component field formalisms with and without auxiliary fields. We show that in both cases the vacuum energy is equal to zero. However, in the formalism where the auxiliary fields are excluded, the vanishing of the vacuum energy arises due to the cancellation between the potential and kinetic energies, while in the formalism with the auxiliary fields, both terms vanish separately.