Laboratoire de Physique Theorique, Univesity of Strasbourg I,

3-5 rue de l'Universit\'e, 67084 Strasbourg cedex, FRANCE

E-mail: rausch@lpt1.u-strasbg.fr

**Cubic supersymmetry in field theory**

**Abstract:**

We consider a four dimensional space-time symmetry which is a non trivial
extension of the Poincar\'e algebra, different from supersymmetry and not
contradicting *a priori* the well-known no-go theorems.
We investigate some field theoretical aspects of this new symmetry and
construct invariant actions for non-interacting fermion and non-interacting
boson multiplets. In the case of the bosonic multiplet, where two-form
fields appear naturally, we find that this symmetry is compatible with
a local *U*(1) gauge symmetry, only when the latter is gauge
fixed by a `t Hooft-Feynman term.