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.
Highlights
The discovery of the supersymmetry – the symmetry between bosons and fermions in the early seventies [1, 2, 3] was one of the most impressive achievements of the modern theoretical physics
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
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
Summary
The discovery of the supersymmetry – the symmetry between bosons and fermions in the early seventies [1, 2, 3] was one of the most impressive achievements of the modern theoretical physics. If we consider the non-supersymmetric models with the Pauli-Zeldovich mechanism of cancellation of UV divergences for the vacuum energy in the presence of interactions, the numbers of the boson and fermion degrees of freedom should coincide on shell, but off shell as well [14]. It looks like the introduction of the auxiliary fields becomes unavoidable even for non-supersymmetric models if we want to make the Pauli-Zeldovich mechanism efficient. Give the vanishing contribution (here Sk(3lm) is a three-vertex corresponding to the cubic interaction term (8)) This follows from the fact that the tadpole diagrams in the Wess-Zumino model are cancelled due to supersymmetry. One can say that both the kinetic vacuum energy and the potential vacuum energy in the Wess-Zumino model with the auxiliary fields are cancelled separately
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