# Non-uniqueness of the supersymmetric extension of the $O(3)$ $\sigma$-model

## TL;DR

This paper investigates the supersymmetric extensions of the $O(3)$ sigma-model in 1+1 and 2+1 dimensions, revealing multiple non-equivalent supersymmetric versions that share the same bosonic sector without higher-derivative terms.

## Contribution

It demonstrates the non-uniqueness of supersymmetric extensions of the $O(3)$ sigma-model, constructing different supersymmetric models with identical bosonic sectors.

## Key findings

- Multiple non-equivalent supersymmetric models with the same bosonic sector.
- Construction of supersymmetric models free from higher-derivative terms.
- Extension of analysis to both 1+1 and 2+1 dimensions.

## Abstract

We study the supersymmetric extensions of the $O(3)$ $\sigma$-model in $1+1$ and $2+1$ dimensions. We show that it is possible to construct non-equivalent supersymmetric versions of a given model sharing the same bosonic sector and free from higher-derivative terms.