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

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.