One-loop effective potential in nonlocal supersymmetric theories

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, $\mathrm{\ensuremath{\Lambda}}$, much greater than any energy scale; in addition, this model also depends on an extra parameter $\ensuremath{\xi}$. As to the other three models, the result looks like the renormalized effective potential for the usual Wess-Zumino model, where the normalization scale $\ensuremath{\mu}$ is replaced by the $\mathrm{\ensuremath{\Lambda}}$. Moreover, the fourth model displays a divergence which can be eliminated through the appropriate wave function renormalization.