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.