Supersymmetric galileons and auxiliary fields in 2+1 dimensions

In this work we study various aspects of supersymmetric three-dimensional higher-derivative field theories. We classify all possible models without derivative terms in the auxiliary field of the fermionic sector and find that scalar field theories of the form $P(X,\varphi )$, where $X=-(\mathrm{\partial }\varphi {)}^2\mathrm{/}2$, belong to this kind of models. A ghost-free supersymmetric extension of Galileon models is found in three spacetime dimensions. Finally, the auxiliary field problem is discussed.