Alternative auxiliary fields for chiral multiplets

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 Kμνρσ and Hμνρσ which are the field strengths of the 3-form potential auxiliary fields Gμνρ and Fμνρ. 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.