Field Theoretic Realizations for Cubic Supersymmetry

We consider a four dimensional space-time symmetry which is a non trivial 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 non-interacting 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. PACS numbers: 03.50.Kk, 03.65.Fd, 11.30.Ly keywords: generalization of supersymmetry, Field Theory, algebraic methods, Lie (super)algebras. e-mail: [email protected] e-mail: [email protected] e-mail: [email protected]