Field Theoretic Realizations for Cubic Supersymmetry

Abstract

We consider a four dimensional space-time symmetry which is a non trivial extension of the Poincaré 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.

LaTex, 25 pages use macro amsmath and amsfonts.Section 5 slightly extended, some references corrected

References in corpus (2)

• Fractional helicity, Lorentz symmetry breaking, compactification and anyons
• Finite-dimensional Lie algebras of order F

Cited by in corpus (13)

• Cubic supersymmetry and abelian gauge invariance
• Hopf algebras for ternary algebras
• Poincaré and sl(2) algebras of order 3
• Kinematical superalgebras and Lie algebras of order 3
• Ternary algebras and groups
• Parafermions for higher order extensions of the Poincaré algebra and their associated superspace
• Parasupersymmetry and N-fold Supersymmetry in Quantum Many-Body Systems I. General Formalism and Second Order
• Filiform Lie algebras of order 3
• Some Results on Cubic and Higher Order Extensions of the Poincaré Algebra
• Cubic extentions of the Poincaré algebra
• Unexpected Features of Supersymmetry with Central Charges
• Nonassociatuve generalization of supersymmetry
• Hidden quartic symmetry in N=2 supersymmetry