Supersymmetry in the O(N) Gross-Neveu Models?

TL;DR

This paper investigates the potential for supersymmetry in O(N) Gross-Neveu models by analyzing a classical current that becomes supersymmetric with quantum anomalies, and explores its algebra and implications.

Contribution

It generalizes a supersymmetric current from the O(3) to the O(N) Gross-Neveu models and examines the conditions for supersymmetry to be established.

Findings

The current becomes supersymmetric when quantum anomalies are included.

The algebra of the current is computed.

The possibility of establishing supersymmetry in these models is discussed.

Abstract

We study a special classical current in the O(3) Gross-Neveu model that becomes supersymmetric when quantum anomalies are included. Following its definition, we generalize the current for the general case, the O(N) Gross-Neveu models. We compute its algebra and discuss the possibility of supersymmetry can be established for these models.