D=(2+1) O(N) Wess-Zumino model in a large N limit

TL;DR

This paper computes the effective Kahlerian superpotential of a massless  O(N) Wess-Zumino model in three dimensions at large N, showing symmetry preservation and no dynamical mass generation.

Contribution

It provides the first large N, two-loop order analysis of the effective superpotential in this model, demonstrating symmetry preservation.

Findings

O(N) symmetry remains unbroken at large N

No dynamical mass generation occurs in the supersymmetric phase

Radiative corrections do not induce spontaneous O(N) symmetry breaking

Abstract

Using the superfield formalism, the effective Kahlerian superpotential of the massless \cal{N}=1 O(N) Wess-Zumino model is computed in the limit of large N, in three spacetime dimensions. The effective Kahlerian superpotential is evaluated at the subleading order in the 1/N expansion, which involves diagrams up to two-loop order, for a small coupling constant. We show that the O(N) symmetry of the model is preserved in this approximation and that no mass is dynamically generated in the supersymmetric phase. We discuss why spontaneous O(N) symmetry breaking cannot be induced by radiative corrections in such model.