Cubic supersymmetry and abelian gauge invariance
Abstract:
We consider a 4 dimensional space-time symmetry, which is a non-trivial
extension of the Poincar\'e algebra. This new symmetry extract "cubic roots"
of translations, hence being different from the supersymmetric extension
and not contradicting the no-go theorems. Some field theoretical aspects
are investigated. Boson multiplets and free Lagrangians are explicitely
built. We also study in detail the interplay between this symmetry and
abelian gauge symmetry.