Field Theoretic Realizations for Cubic Supersymmetry

TL;DR

This paper explores a novel four-dimensional space-time symmetry extending the Poincaré algebra, distinct from supersymmetry, and constructs invariant actions for fermion and boson multiplets, revealing compatibility with gauge fixing.

Contribution

It introduces a new symmetry extension of the Poincaré algebra and develops invariant field actions, expanding the understanding of space-time symmetries beyond supersymmetry.

Findings

Constructed invariant actions for fermion and boson multiplets.

Found compatibility of the symmetry with gauge fixing in bosonic multiplets.

Demonstrated the symmetry's consistency with local U(1) gauge symmetry.

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 {\sl 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.