On the one-loop effective potential in nonlocal supersymmetric theories

TL;DR

This paper investigates the one-loop effective potential in various nonlocal supersymmetric models, extending the Wess-Zumino model, and analyzes their low-energy quantum corrections and renormalization properties.

Contribution

It introduces four nonlocal supersymmetric models, analyzing their effective potentials and renormalization behavior, highlighting differences from the standard Wess-Zumino model.

Findings

Only one model reduces to the standard Wess-Zumino model at high nonlocality scale.

Three models have effective potentials similar to the Wess-Zumino model with a modified scale.

One model exhibits divergences that can be removed via wave function renormalization.

Abstract

Within the superfield approach, we consider the nonlocal generalization of the Wess-Zumino model and calculate the one-loop low-energy contributions to the effective action. Four different nonlocal models are considered, among which only the first model does not reduce to the standard Wess-Zumino model when we take the parameter of nonlocality of the model, $\Lambda$, much greater than any energy scale; in addition, this model also depends on an extra parameter, $\xi$. As to the other three models, the result looks like the renormalized effective potential for the usual Wess-Zumino model, where the normalization scale $\mu$ is replaced by the $\Lambda$. Moreover, the fourth model displays a divergence which can be eliminated through the appropriate wave function renormalization.