Two-loop effective potential for the Wess-Zumino model in 2+1 dimensions

TL;DR

This paper calculates the two-loop effective potential of the 2+1 dimensional $ =1$ Wess-Zumino model using superfield techniques, demonstrating supersymmetry remains unbroken and the model is infrared free.

Contribution

It provides the first two-loop off-shell effective potential calculation for this model, analyzing supersymmetry, mass generation, and renormalization group functions.

Findings

Supersymmetry is not dynamically broken.

No perturbative dynamical mass generation occurs.

The model is infrared free with specific gamma and beta functions.

Abstract

By using superfield techniques, the effective potential of the $\mathcal{N}=1$ Wess-Zumino model in 2+1 dimensions is computed off-shell up to two loops. It is shown that supersymmetry is not dynamically broken, and that dynamical generation of mass does not occur perturbatively. We also investigate the renormalization of the effective potential and determine the renormalization group gamma and beta functions, showing that this model is infrared free. Comparison with some other results in the literature is provided.