Alternative auxiliary fields for chiral multiplets

Abstract

We study 3-form auxiliary field formulation for chiral multiplets in the Wess-Zumino model. The conventional auxiliary fields $F$ and $G$ are replaced by their Hodge duals ${K}_{\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\rho}\ensuremath{\sigma}}$ and ${H}_{\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\rho}\ensuremath{\sigma}}$ which are the field strengths of the 3-form potential auxiliary fields ${G}_{\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\rho}}$ and ${F}_{\ensuremath{\mu}\ensuremath{\nu}\ensuremath{\rho}}$. Even though duality transformations connect these two formulations, there exist certain differences from the conventional formulation. When boundary conditions are taken into account, the field equations in the 3-form formulation are equivalent to the conventional ones, while our Lagrangian is not. We also show that the new field strengths acquire generalized Chern-Simons terms. The O'Raifeartaigh mechanism works for spontaneous supersymmetry breaking also in the 3-form auxiliary field formulation via the boundary conditions on the 3-form auxiliary fields.