FIELD THEORETIC REALIZATIONS FOR CUBIC SUPERSYMMETRY

Abstract

We consider a four-dimensional space–time symmetry which is a nontrivial extension of the Poincaré 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 noninteracting fermion and noninteracting 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.