Gauging internal fermionic symmetries and spin 3/2 fields

Field theoretic models possessing a global internal fermionic shift symmetry are considered. When such a symmetry is realized locally, spin 3/2 fields appear naturally as gauge fields. Implementation of the gauging procedure requires not only the usual replacement of ordinary derivatives by covariant derivatives containing the spin 3/2 fields, but also the inclusion of additional monomials. The Higgs mechanism and the high energy Nambu-Goldstone fermion equivalence theorem are explicitly demonstrated. ∗e-mail address: [email protected] Spin 1 fields arise most naturally as the vector connections when global internal symmetries are realized as local symmmetries. This gauging of global symmetries and the resultant Higgs mechanism is at the heart of the much of particle physics including the Standard Model. In this note, we address the possibility of the origin of spin 3/2 particles as the result of gauging a global internal fermionic symmetry. The most familiar fermionic symmetry is supersymmetry (SUSY), a spacetime symmetry related through the SUSY algebra to spacetime translations. Thus gauging supersymmetry automatically requires a gauging of the full Poincaré group resulting in a supergravity theory which, in addition to the spin 3/2 fields, necessarily contains the spin 2 graviton field. Here we examine models with a global internal fermionic symmetry whose gauging can be implemented only using the spin 3/2 fields without the need for any other higher spin fields. We begin by introducing a model which contains a 2-component Weyl fermion, λ and its complex conjugate λ̄α̇ and demand the model be invariant under the global shift transformation: δ(ξ, ξ̄)λ = f ξ δ(ξ, ξ̄)λ̄ = f ξ̄ (1) where ξ, ξ̄ are spacetime independent Grassmann parameters and f is a mass scale. The resulting invariant action, retaining terms through mass dimension 4 is just the kinetic term of the free Dirac action: I0 = ∫ dxL0 ; L0 = − i 2 λσ ↔ ∂μ λ̄ (2) Note that the required symmetry forbids a λλ+ λ̄λ̄ fermion mass term. The globally symmetric model can be readily extended to include higher dimensional (derivatively coupled) fermionic self interations. In fact, any term of the form L1 = λσ∂μF̄1(∂λ, ∂λ̄) + h.c. (3) where F̄ α̇ 1 (∂λ, ∂λ̄) is a function of ∂λ and ∂λ̄ produces an invariant action. An example of such an operator is provided by F̄ α̇ 1 = a1 f2 ∂λ̄, where a1 is a constant. The model can be further extended to include couplings to other fields (generically referred to as φi). Under the global shift of the fermion field, all these other fields are taken