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

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.

19 pages